x+8/10x=180

Solution for x+8/10x=180 equation:

x+8/10x=180

We move all terms to the left:

x+8/10x-(180)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We multiply all the terms by the denominator


x*10x-180*10x+8=0

Wy multiply elements

10x^2-1800x+8=0

a = 10; b = -1800; c = +8;
Δ = b2-4ac
Δ = -18002-4·10·8
Δ = 3239680
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:

$\sqrt{\Delta}=\sqrt{3239680}=\sqrt{256*12655}=\sqrt{256}*\sqrt{12655}=16\sqrt{12655}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1800)-16\sqrt{12655}}{2*10}=\frac{1800-16\sqrt{12655}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1800)+16\sqrt{12655}}{2*10}=\frac{1800+16\sqrt{12655}}{20}
$