(5x+3)(17+3x)=180

Solution for (5x+3)(17+3x)=180 equation:

(5x+3)(17+3x)=180

We move all terms to the left:

(5x+3)(17+3x)-(180)=0

We add all the numbers together, and all the variables

(5x+3)(3x+17)-180=0

We multiply parentheses ..

(+15x^2+85x+9x+51)-180=0

We get rid of parentheses

15x^2+85x+9x+51-180=0

We add all the numbers together, and all the variables

15x^2+94x-129=0

a = 15; b = 94; c = -129;
Δ = b2-4ac
Δ = 942-4·15·(-129)
Δ = 16576
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:

$\sqrt{\Delta}=\sqrt{16576}=\sqrt{64*259}=\sqrt{64}*\sqrt{259}=8\sqrt{259}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(94)-8\sqrt{259}}{2*15}=\frac{-94-8\sqrt{259}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(94)+8\sqrt{259}}{2*15}=\frac{-94+8\sqrt{259}}{30}
$