(X+15)(5x-7)=(3x+5)

Solution for (X+15)(5x-7)=(3x+5) equation:

(X+15)(5X-7)=(3X+5)

We move all terms to the left:

(X+15)(5X-7)-((3X+5))=0

We multiply parentheses ..

(+5X^2-7X+75X-105)-((3X+5))=0


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

(3X+5)

We get rid of parentheses

3X+5

Back to the equation:

-(3X+5)


We get rid of parentheses

5X^2-7X+75X-3X-105-5=0

We add all the numbers together, and all the variables

5X^2+65X-110=0

a = 5; b = 65; c = -110;
Δ = b2-4ac
Δ = 652-4·5·(-110)
Δ = 6425
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6425}=\sqrt{25*257}=\sqrt{25}*\sqrt{257}=5\sqrt{257}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-5\sqrt{257}}{2*5}=\frac{-65-5\sqrt{257}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+5\sqrt{257}}{2*5}=\frac{-65+5\sqrt{257}}{10}
$