(5x+57)(x+15)=90

Solution for (5x+57)(x+15)=90 equation:

(5x+57)(x+15)=90

We move all terms to the left:

(5x+57)(x+15)-(90)=0

We multiply parentheses ..

(+5x^2+75x+57x+855)-90=0

We get rid of parentheses

5x^2+75x+57x+855-90=0

We add all the numbers together, and all the variables

5x^2+132x+765=0

a = 5; b = 132; c = +765;
Δ = b2-4ac
Δ = 1322-4·5·765
Δ = 2124
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:

$\sqrt{\Delta}=\sqrt{2124}=\sqrt{36*59}=\sqrt{36}*\sqrt{59}=6\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(132)-6\sqrt{59}}{2*5}=\frac{-132-6\sqrt{59}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(132)+6\sqrt{59}}{2*5}=\frac{-132+6\sqrt{59}}{10}
$