X(2y-5)=y+5

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

X(2X-5)=X+5

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

2X^2-5X-X-5=0

We add all the numbers together, and all the variables

2X^2-6X-5=0

a = 2; b = -6; c = -5;
Δ = b2-4ac
Δ = -62-4·2·(-5)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{19}}{2*2}=\frac{6-2\sqrt{19}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{19}}{2*2}=\frac{6+2\sqrt{19}}{4}
$