5x(2x-4)=2(8x-10)

Solution for 5x(2x-4)=2(8x-10) equation:

5x(2x-4)=2(8x-10)

We move all terms to the left:

5x(2x-4)-(2(8x-10))=0

We multiply parentheses

10x^2-20x-(2(8x-10))=0


We calculate terms in parentheses: -(2(8x-10)), so:

2(8x-10)

We multiply parentheses

16x-20

Back to the equation:

-(16x-20)


We get rid of parentheses

10x^2-20x-16x+20=0

We add all the numbers together, and all the variables

10x^2-36x+20=0

a = 10; b = -36; c = +20;
Δ = b2-4ac
Δ = -362-4·10·20
Δ = 496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{31}}{2*10}=\frac{36-4\sqrt{31}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{31}}{2*10}=\frac{36+4\sqrt{31}}{20}
$