11x(x-5)=10x(x+5)

Solution for 11x(x-5)=10x(x+5) equation:

11x(x-5)=10x(x+5)

We move all terms to the left:

11x(x-5)-(10x(x+5))=0

We multiply parentheses

11x^2-55x-(10x(x+5))=0


We calculate terms in parentheses: -(10x(x+5)), so:

10x(x+5)

We multiply parentheses

10x^2+50x

Back to the equation:

-(10x^2+50x)


We get rid of parentheses

11x^2-10x^2-55x-50x=0

We add all the numbers together, and all the variables

x^2-105x=0

a = 1; b = -105; c = 0;
Δ = b2-4ac
Δ = -1052-4·1·0
Δ = 11025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11025}=105$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-105}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+105}{2*1}=\frac{210}{2}
=105
$