(10x-20)+(x+52)+(1/8x+59)=180

Solution for (10x-20)+(x+52)+(1/8x+59)=180 equation:

(10x-20)+(x+52)+(1/8x+59)=180

We move all terms to the left:

(10x-20)+(x+52)+(1/8x+59)-(180)=0


Domain of the equation: 8x+59)!=0

x∈R


We get rid of parentheses

10x+x+1/8x-20+52+59-180=0

We multiply all the terms by the denominator


10x*8x+x*8x-20*8x+52*8x+59*8x-180*8x+1=0

Wy multiply elements

80x^2+8x^2-160x+416x+472x-1440x+1=0

We add all the numbers together, and all the variables

88x^2-712x+1=0

a = 88; b = -712; c = +1;
Δ = b2-4ac
Δ = -7122-4·88·1
Δ = 506592
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:

$\sqrt{\Delta}=\sqrt{506592}=\sqrt{144*3518}=\sqrt{144}*\sqrt{3518}=12\sqrt{3518}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-712)-12\sqrt{3518}}{2*88}=\frac{712-12\sqrt{3518}}{176}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-712)+12\sqrt{3518}}{2*88}=\frac{712+12\sqrt{3518}}{176}
$