x+5/7x+20=180

Solution for x+5/7x+20=180 equation:

x+5/7x+20=180

We move all terms to the left:

x+5/7x+20-(180)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

x+5/7x-160=0

We multiply all the terms by the denominator


x*7x-160*7x+5=0

Wy multiply elements

7x^2-1120x+5=0

a = 7; b = -1120; c = +5;
Δ = b2-4ac
Δ = -11202-4·7·5
Δ = 1254260
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:

$\sqrt{\Delta}=\sqrt{1254260}=\sqrt{1156*1085}=\sqrt{1156}*\sqrt{1085}=34\sqrt{1085}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1120)-34\sqrt{1085}}{2*7}=\frac{1120-34\sqrt{1085}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1120)+34\sqrt{1085}}{2*7}=\frac{1120+34\sqrt{1085}}{14}
$