(4x+15)(12x-5)=90

Solution for (4x+15)(12x-5)=90 equation:

(4x+15)(12x-5)=90

We move all terms to the left:

(4x+15)(12x-5)-(90)=0

We multiply parentheses ..

(+48x^2-20x+180x-75)-90=0

We get rid of parentheses

48x^2-20x+180x-75-90=0

We add all the numbers together, and all the variables

48x^2+160x-165=0

a = 48; b = 160; c = -165;
Δ = b2-4ac
Δ = 1602-4·48·(-165)
Δ = 57280
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:

$\sqrt{\Delta}=\sqrt{57280}=\sqrt{64*895}=\sqrt{64}*\sqrt{895}=8\sqrt{895}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-8\sqrt{895}}{2*48}=\frac{-160-8\sqrt{895}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+8\sqrt{895}}{2*48}=\frac{-160+8\sqrt{895}}{96}
$