(x+38)(2x-7)=180

Solution for (x+38)(2x-7)=180 equation:

(x+38)(2x-7)=180

We move all terms to the left:

(x+38)(2x-7)-(180)=0

We multiply parentheses ..

(+2x^2-7x+76x-266)-180=0

We get rid of parentheses

2x^2-7x+76x-266-180=0

We add all the numbers together, and all the variables

2x^2+69x-446=0

a = 2; b = 69; c = -446;
Δ = b2-4ac
Δ = 692-4·2·(-446)
Δ = 8329
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{-(69)-\sqrt{8329}}{2*2}=\frac{-69-\sqrt{8329}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+\sqrt{8329}}{2*2}=\frac{-69+\sqrt{8329}}{4}
$