2x2=12x-16

Solution for 2x2=12x-16 equation:

2x^2=12x-16

We move all terms to the left:

2x^2-(12x-16)=0

We get rid of parentheses

2x^2-12x+16=0

a = 2; b = -12; c = +16;
Δ = b2-4ac
Δ = -122-4·2·16
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{-(-12)-4}{2*2}=\frac{8}{4}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4}{2*2}=\frac{16}{4}
=4
$