(90/x-0.75)*(x+10)=90

Solution for (90/x-0.75)*(x+10)=90 equation:

(90/x-0.75)(x+10)=90

We move all terms to the left:

(90/x-0.75)(x+10)-(90)=0


Domain of the equation: x-0.75)(x+10)!=0

x∈R


We multiply parentheses ..

(+90x^2+900x-0.75x-7.5)-90=0

We get rid of parentheses

90x^2+900x-0.75x-7.5-90=0

We add all the numbers together, and all the variables

90x^2+899.25x-97.5=0

a = 90; b = 899.25; c = -97.5;
Δ = b2-4ac
Δ = 899.252-4·90·(-97.5)
Δ = 843750.5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(899.25)-\sqrt{843750.5625}}{2*90}=\frac{-899.25-\sqrt{843750.5625}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(899.25)+\sqrt{843750.5625}}{2*90}=\frac{-899.25+\sqrt{843750.5625}}{180}
$