(x-3)-2(x+6)x=-5

Solution for (x-3)-2(x+6)x=-5 equation:

(x-3)-2(x+6)x=-5

We move all terms to the left:

(x-3)-2(x+6)x-(-5)=0

We add all the numbers together, and all the variables

(x-3)-2(x+6)x+5=0

We multiply parentheses

-2x^2+(x-3)-12x+5=0

We get rid of parentheses

-2x^2+x-12x-3+5=0

We add all the numbers together, and all the variables

-2x^2-11x+2=0

a = -2; b = -11; c = +2;
Δ = b2-4ac
Δ = -112-4·(-2)·2
Δ = 137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{137}}{2*-2}=\frac{11-\sqrt{137}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{137}}{2*-2}=\frac{11+\sqrt{137}}{-4}
$