(3x+5)(2x-15)=90

Solution for (3x+5)(2x-15)=90 equation:

(3x+5)(2x-15)=90

We move all terms to the left:

(3x+5)(2x-15)-(90)=0

We multiply parentheses ..

(+6x^2-45x+10x-75)-90=0

We get rid of parentheses

6x^2-45x+10x-75-90=0

We add all the numbers together, and all the variables

6x^2-35x-165=0

a = 6; b = -35; c = -165;
Δ = b2-4ac
Δ = -352-4·6·(-165)
Δ = 5185
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{-(-35)-\sqrt{5185}}{2*6}=\frac{35-\sqrt{5185}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{5185}}{2*6}=\frac{35+\sqrt{5185}}{12}
$