x(3x+5)+75=180

Solution for x(3x+5)+75=180 equation:

x(3x+5)+75=180

We move all terms to the left:

x(3x+5)+75-(180)=0

We add all the numbers together, and all the variables

x(3x+5)-105=0

We multiply parentheses

3x^2+5x-105=0

a = 3; b = 5; c = -105;
Δ = b2-4ac
Δ = 52-4·3·(-105)
Δ = 1285
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{1285}}{2*3}=\frac{-5-\sqrt{1285}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{1285}}{2*3}=\frac{-5+\sqrt{1285}}{6}
$