2x^2=28x-96

Solution for 2x^2=28x-96 equation:

2x^2=28x-96

We move all terms to the left:

2x^2-(28x-96)=0

We get rid of parentheses

2x^2-28x+96=0

a = 2; b = -28; c = +96;
Δ = b2-4ac
Δ = -282-4·2·96
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4}{2*2}=\frac{24}{4}
=6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4}{2*2}=\frac{32}{4}
=8
$