5x(2-x)=8x(7-5x)

Solution for 5x(2-x)=8x(7-5x) equation:

5x(2-x)=8x(7-5x)

We move all terms to the left:

5x(2-x)-(8x(7-5x))=0

We add all the numbers together, and all the variables

5x(-1x+2)-(8x(-5x+7))=0

We multiply parentheses

-5x^2+10x-(8x(-5x+7))=0


We calculate terms in parentheses: -(8x(-5x+7)), so:

8x(-5x+7)

We multiply parentheses

-40x^2+56x

Back to the equation:

-(-40x^2+56x)


We get rid of parentheses

-5x^2+40x^2-56x+10x=0

We add all the numbers together, and all the variables

35x^2-46x=0

a = 35; b = -46; c = 0;
Δ = b2-4ac
Δ = -462-4·35·0
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-46}{2*35}=\frac{0}{70}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+46}{2*35}=\frac{92}{70}
=1+11/35
$