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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+3x^2+9x+5x+15)-180=0

We get rid of parentheses

3x^2+9x+5x+15-180=0

We add all the numbers together, and all the variables

3x^2+14x-165=0

a = 3; b = 14; c = -165;
Δ = b2-4ac
Δ = 142-4·3·(-165)
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-8\sqrt{34}}{2*3}=\frac{-14-8\sqrt{34}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+8\sqrt{34}}{2*3}=\frac{-14+8\sqrt{34}}{6}
$