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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply parentheses ..

(+x^2+6x-3x-18)+5x=0

We get rid of parentheses

x^2+6x-3x+5x-18=0

We add all the numbers together, and all the variables

x^2+8x-18=0

a = 1; b = 8; c = -18;
Δ = b2-4ac
Δ = 82-4·1·(-18)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{34}}{2*1}=\frac{-8-2\sqrt{34}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{34}}{2*1}=\frac{-8+2\sqrt{34}}{2}
$