2x(x-6)=5x(x+10)

Solution for 2x(x-6)=5x(x+10) equation:

2x(x-6)=5x(x+10)

We move all terms to the left:

2x(x-6)-(5x(x+10))=0

We multiply parentheses

2x^2-12x-(5x(x+10))=0


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

5x(x+10)

We multiply parentheses

5x^2+50x

Back to the equation:

-(5x^2+50x)


We get rid of parentheses

2x^2-5x^2-12x-50x=0

We add all the numbers together, and all the variables

-3x^2-62x=0

a = -3; b = -62; c = 0;
Δ = b2-4ac
Δ = -622-4·(-3)·0
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-62}{2*-3}=\frac{0}{-6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+62}{2*-3}=\frac{124}{-6}
=-20+2/3
$