-2x(x-6)+8=4x-10

Solution for -2x(x-6)+8=4x-10 equation:

-2x(x-6)+8=4x-10

We move all terms to the left:

-2x(x-6)+8-(4x-10)=0

We multiply parentheses

-2x^2+12x-(4x-10)+8=0

We get rid of parentheses

-2x^2+12x-4x+10+8=0

We add all the numbers together, and all the variables

-2x^2+8x+18=0

a = -2; b = 8; c = +18;
Δ = b2-4ac
Δ = 82-4·(-2)·18
Δ = 208
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{13}}{2*-2}=\frac{-8-4\sqrt{13}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{13}}{2*-2}=\frac{-8+4\sqrt{13}}{-4}
$