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.

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}}

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).