(2x+7)(x-1)=180

Solution for (2x+7)(x-1)=180 equation:

(2x+7)(x-1)=180

We move all terms to the left:

(2x+7)(x-1)-(180)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+5x-187=0

a = 2; b = 5; c = -187;
Δ = b2-4ac
Δ = 52-4·2·(-187)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-39}{2*2}=\frac{-44}{4}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+39}{2*2}=\frac{34}{4}
=8+1/2
$