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

Solution for X(2x+3)-5(2x+3)=0 equation:

X(2X+3)-5(2X+3)=0

We multiply parentheses

2X^2+3X-10X-15=0

We add all the numbers together, and all the variables

2X^2-7X-15=0

a = 2; b = -7; c = -15;
Δ = b2-4ac
Δ = -72-4·2·(-15)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*2}=\frac{-6}{4}
=-1+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*2}=\frac{20}{4}
=5
$