x/20x+10=5x+85

Solution for x/20x+10=5x+85 equation:

x/20x+10=5x+85

We move all terms to the left:

x/20x+10-(5x+85)=0


Domain of the equation: 20x!=0

x!=0/20

x!=0

x∈R


We get rid of parentheses

x/20x-5x-85+10=0

We multiply all the terms by the denominator


x-5x*20x-85*20x+10*20x=0

Wy multiply elements

-100x^2+x-1700x+200x=0

We add all the numbers together, and all the variables

-100x^2-1499x=0

a = -100; b = -1499; c = 0;
Δ = b2-4ac
Δ = -14992-4·(-100)·0
Δ = 2247001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2247001}=1499$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1499)-1499}{2*-100}=\frac{0}{-200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1499)+1499}{2*-100}=\frac{2998}{-200}
=-14+99/100
$