(2x-5)(x+1)=72

Solution for (2x-5)(x+1)=72 equation:

(2x-5)(x+1)=72

We move all terms to the left:

(2x-5)(x+1)-(72)=0

We multiply parentheses ..

(+2x^2+2x-5x-5)-72=0

We get rid of parentheses

2x^2+2x-5x-5-72=0

We add all the numbers together, and all the variables

2x^2-3x-77=0

a = 2; b = -3; c = -77;
Δ = b2-4ac
Δ = -32-4·2·(-77)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-25}{2*2}=\frac{-22}{4}
=-5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+25}{2*2}=\frac{28}{4}
=7
$