15x^2+70x+75=180

Solution for 15x^2+70x+75=180 equation:

15x^2+70x+75=180

We move all terms to the left:

15x^2+70x+75-(180)=0

We add all the numbers together, and all the variables

15x^2+70x-105=0

a = 15; b = 70; c = -105;
Δ = b2-4ac
Δ = 702-4·15·(-105)
Δ = 11200
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:

$\sqrt{\Delta}=\sqrt{11200}=\sqrt{1600*7}=\sqrt{1600}*\sqrt{7}=40\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-40\sqrt{7}}{2*15}=\frac{-70-40\sqrt{7}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+40\sqrt{7}}{2*15}=\frac{-70+40\sqrt{7}}{30}
$