(3x+13)(5x+9)=90

Solution for (3x+13)(5x+9)=90 equation:

(3x+13)(5x+9)=90

We move all terms to the left:

(3x+13)(5x+9)-(90)=0

We multiply parentheses ..

(+15x^2+27x+65x+117)-90=0

We get rid of parentheses

15x^2+27x+65x+117-90=0

We add all the numbers together, and all the variables

15x^2+92x+27=0

a = 15; b = 92; c = +27;
Δ = b2-4ac
Δ = 922-4·15·27
Δ = 6844
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:

$\sqrt{\Delta}=\sqrt{6844}=\sqrt{4*1711}=\sqrt{4}*\sqrt{1711}=2\sqrt{1711}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-2\sqrt{1711}}{2*15}=\frac{-92-2\sqrt{1711}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+2\sqrt{1711}}{2*15}=\frac{-92+2\sqrt{1711}}{30}
$