x+10+50/x=70-8x

Solution for x+10+50/x=70-8x equation:

x+10+50/x=70-8x

We move all terms to the left:

x+10+50/x-(70-8x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+50/x-(-8x+70)+10=0

We get rid of parentheses

x+50/x+8x-70+10=0

We multiply all the terms by the denominator


x*x+8x*x-70*x+10*x+50=0

We add all the numbers together, and all the variables

-60x+x*x+8x*x+50=0

Wy multiply elements

x^2+8x^2-60x+50=0

We add all the numbers together, and all the variables

9x^2-60x+50=0

a = 9; b = -60; c = +50;
Δ = b2-4ac
Δ = -602-4·9·50
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-30\sqrt{2}}{2*9}=\frac{60-30\sqrt{2}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+30\sqrt{2}}{2*9}=\frac{60+30\sqrt{2}}{18}
$