(7/2x+4)+(8x-8)=180

Solution for (7/2x+4)+(8x-8)=180 equation:

(7/2x+4)+(8x-8)=180

We move all terms to the left:

(7/2x+4)+(8x-8)-(180)=0


Domain of the equation: 2x+4)!=0

x∈R


We get rid of parentheses

7/2x+8x+4-8-180=0

We multiply all the terms by the denominator


8x*2x+4*2x-8*2x-180*2x+7=0

Wy multiply elements

16x^2+8x-16x-360x+7=0

We add all the numbers together, and all the variables

16x^2-368x+7=0

a = 16; b = -368; c = +7;
Δ = b2-4ac
Δ = -3682-4·16·7
Δ = 134976
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:

$\sqrt{\Delta}=\sqrt{134976}=\sqrt{64*2109}=\sqrt{64}*\sqrt{2109}=8\sqrt{2109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-368)-8\sqrt{2109}}{2*16}=\frac{368-8\sqrt{2109}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-368)+8\sqrt{2109}}{2*16}=\frac{368+8\sqrt{2109}}{32}
$