X^2+3x+5x+15=180

Solution for X^2+3x+5x+15=180 equation:

X^2+3X+5X+15=180

We move all terms to the left:

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

We add all the numbers together, and all the variables

X^2+8X-165=0

a = 1; b = 8; c = -165;
Δ = b2-4ac
Δ = 82-4·1·(-165)
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{181}}{2*1}=\frac{-8-2\sqrt{181}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{181}}{2*1}=\frac{-8+2\sqrt{181}}{2}
$