2x(-5+6x)=10x(8-5x)=0

Solution for 2x(-5+6x)=10x(8-5x)=0 equation:

2x(-5+6x)=10x(8-5x)=0

We move all terms to the left:

2x(-5+6x)-(10x(8-5x))=0

We add all the numbers together, and all the variables

2x(6x-5)-(10x(-5x+8))=0

We multiply parentheses

12x^2-10x-(10x(-5x+8))=0


We calculate terms in parentheses: -(10x(-5x+8)), so:

10x(-5x+8)

We multiply parentheses

-50x^2+80x

Back to the equation:

-(-50x^2+80x)


We get rid of parentheses

12x^2+50x^2-80x-10x=0

We add all the numbers together, and all the variables

62x^2-90x=0

a = 62; b = -90; c = 0;
Δ = b2-4ac
Δ = -902-4·62·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-90}{2*62}=\frac{0}{124}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+90}{2*62}=\frac{180}{124}
=1+14/31
$