x-1800/x=90

Solution for x-1800/x=90 equation:

x-1800/x=90

We move all terms to the left:

x-1800/x-(90)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-90*x-1800=0

We add all the numbers together, and all the variables

-90x+x*x-1800=0

Wy multiply elements

x^2-90x-1800=0

a = 1; b = -90; c = -1800;
Δ = b2-4ac
Δ = -902-4·1·(-1800)
Δ = 15300
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:

$\sqrt{\Delta}=\sqrt{15300}=\sqrt{900*17}=\sqrt{900}*\sqrt{17}=30\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-30\sqrt{17}}{2*1}=\frac{90-30\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+30\sqrt{17}}{2*1}=\frac{90+30\sqrt{17}}{2}
$