X(2x-10)=(x+10)

Solution for X(2x-10)=(x+10) equation:

X(2X-10)=(X+10)

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -((X+10)), so:

(X+10)

We get rid of parentheses

X+10

Back to the equation:

-(X+10)


We get rid of parentheses

2X^2-10X-X-10=0

We add all the numbers together, and all the variables

2X^2-11X-10=0

a = 2; b = -11; c = -10;
Δ = b2-4ac
Δ = -112-4·2·(-10)
Δ = 201
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{201}}{2*2}=\frac{11-\sqrt{201}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{201}}{2*2}=\frac{11+\sqrt{201}}{4}
$