(6x+40)+2x^2=180

Solution for (6x+40)+2x^2=180 equation:

(6x+40)+2x^2=180

We move all terms to the left:

(6x+40)+2x^2-(180)=0

We get rid of parentheses

2x^2+6x+40-180=0

We add all the numbers together, and all the variables

2x^2+6x-140=0

a = 2; b = 6; c = -140;
Δ = b2-4ac
Δ = 62-4·2·(-140)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-34}{2*2}=\frac{-40}{4}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+34}{2*2}=\frac{28}{4}
=7
$