(X-13)-(x-5)2x=0

Solution for (X-13)-(x-5)2x=0 equation:

(X-13)-(X-5)2X=0

We multiply parentheses

-2X^2+(X-13)+10X=0

We get rid of parentheses

-2X^2+X+10X-13=0

We add all the numbers together, and all the variables

-2X^2+11X-13=0

a = -2; b = 11; c = -13;
Δ = b2-4ac
Δ = 112-4·(-2)·(-13)
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{17}}{2*-2}=\frac{-11-\sqrt{17}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{17}}{2*-2}=\frac{-11+\sqrt{17}}{-4}
$