(x-5)(2x+3)=7

Solution for (x-5)(2x+3)=7 equation:

(x-5)(2x+3)=7

We move all terms to the left:

(x-5)(2x+3)-(7)=0

We multiply parentheses ..

(+2x^2+3x-10x-15)-7=0

We get rid of parentheses

2x^2+3x-10x-15-7=0

We add all the numbers together, and all the variables

2x^2-7x-22=0

a = 2; b = -7; c = -22;
Δ = b2-4ac
Δ = -72-4·2·(-22)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-15}{2*2}=\frac{-8}{4}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+15}{2*2}=\frac{22}{4}
=5+1/2
$