(x+1)(2x-3)=75

Solution for (x+1)(2x-3)=75 equation:

(x+1)(2x-3)=75

We move all terms to the left:

(x+1)(2x-3)-(75)=0

We multiply parentheses ..

(+2x^2-3x+2x-3)-75=0

We get rid of parentheses

2x^2-3x+2x-3-75=0

We add all the numbers together, and all the variables

2x^2-1x-78=0

a = 2; b = -1; c = -78;
Δ = b2-4ac
Δ = -12-4·2·(-78)
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{-(-1)-25}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+25}{2*2}=\frac{26}{4}
=6+1/2
$