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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+2X^2+3X-4X-6)-(5(X-2))=0


We calculate terms in parentheses: -(5(X-2)), so:

5(X-2)

We multiply parentheses

5X-10

Back to the equation:

-(5X-10)


We get rid of parentheses

2X^2+3X-4X-5X-6+10=0

We add all the numbers together, and all the variables

2X^2-6X+4=0

a = 2; b = -6; c = +4;
Δ = b2-4ac
Δ = -62-4·2·4
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2}{2*2}=\frac{4}{4}
=1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2}{2*2}=\frac{8}{4}
=2
$