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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+6x^2-15x+12x-30)-5=0

We get rid of parentheses

6x^2-15x+12x-30-5=0

We add all the numbers together, and all the variables

6x^2-3x-35=0

a = 6; b = -3; c = -35;
Δ = b2-4ac
Δ = -32-4·6·(-35)
Δ = 849
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{-(-3)-\sqrt{849}}{2*6}=\frac{3-\sqrt{849}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{849}}{2*6}=\frac{3+\sqrt{849}}{12}
$