Quadratic Formula - Algebra Step by Step

Solve ax²+bx+c=0 using x=(-b±√(b²-4ac))/(2a). Compute the discriminant b²-4ac first to find the square root, then evaluate the two roots separately on their own lines.

quadratic-formula The formula works for any quadratic. Compute disc=b²-4ac, then the two roots x=(-b+√disc)/(2a) and x=(-b-√disc)/(2a).

Example

Substitute into the quadratic formula, compute the discriminant, then use both signs.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

2x^{2} - 7x + 3 = 0

Step 2 — Substitute

Substitute a = 2, b = -7, c = 3.

x=\frac{ \hl{7} \pm\sqrt{ \hl{49} - \hl{24} }}{ \hl{4} }

Step 3 — Discriminant

Compute the discriminant: 49 - 24 = 25.

49 - 24 = \hl{25}

Step 4 — Simplify radical

Simplify the radical: numerator 7 plus or minus 5, over 4.

x=\frac{ 7 \pm \hl{5} }{ 4 }

Step 5 — Plus root

Use plus: (7 + 5) / 4 = 3.

x= ( 7 + 5 )/ 4 = \hl{3}

Step 6 — Minus root

Use minus: (7 - 5) / 4 = 1/2.

x= ( 7 - 5 )/ 4 = \hlmath{\frac{1}{2}}