(x+42)+(2x-6)x=180

Solution for (x+42)+(2x-6)x=180 equation:

(x+42)+(2x-6)x=180

We move all terms to the left:

(x+42)+(2x-6)x-(180)=0

We multiply parentheses

2x^2+(x+42)-6x-180=0

We get rid of parentheses

2x^2+x-6x+42-180=0

We add all the numbers together, and all the variables

2x^2-5x-138=0

a = 2; b = -5; c = -138;
Δ = b2-4ac
Δ = -52-4·2·(-138)
Δ = 1129
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{1129}}{2*2}=\frac{5-\sqrt{1129}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{1129}}{2*2}=\frac{5+\sqrt{1129}}{4}
$