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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply parentheses

x/5x-8x+16-10=0

We multiply all the terms by the denominator


x-8x*5x+16*5x-10*5x=0

Wy multiply elements

-40x^2+x+80x-50x=0

We add all the numbers together, and all the variables

-40x^2+31x=0

a = -40; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-40)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*-40}=\frac{-62}{-80}
=31/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-40}=\frac{0}{-80}
=0
$