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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+2X^2-5X+10X-25)-(3(X+5))=0


We calculate terms in parentheses: -(3(X+5)), so:

3(X+5)

We multiply parentheses

3X+15

Back to the equation:

-(3X+15)


We get rid of parentheses

2X^2-5X+10X-3X-25-15=0

We add all the numbers together, and all the variables

2X^2+2X-40=0

a = 2; b = 2; c = -40;
Δ = b2-4ac
Δ = 22-4·2·(-40)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-18}{2*2}=\frac{-20}{4}
=-5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+18}{2*2}=\frac{16}{4}
=4
$