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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+3x^2-15x+6x-30)-5=0

We get rid of parentheses

3x^2-15x+6x-30-5=0

We add all the numbers together, and all the variables

3x^2-9x-35=0

a = 3; b = -9; c = -35;
Δ = b2-4ac
Δ = -92-4·3·(-35)
Δ = 501
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{-(-9)-\sqrt{501}}{2*3}=\frac{9-\sqrt{501}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{501}}{2*3}=\frac{9+\sqrt{501}}{6}
$