7.5x-3600/x=210

Solution for 7.5x-3600/x=210 equation:

7.5x-3600/x=210

We move all terms to the left:

7.5x-3600/x-(210)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


(7.5x)*x-210*x-3600=0

We add all the numbers together, and all the variables

(+7.5x)*x-210*x-3600=0

We add all the numbers together, and all the variables

-210x+(+7.5x)*x-3600=0

We multiply parentheses

7x^2-210x-3600=0

a = 7; b = -210; c = -3600;
Δ = b2-4ac
Δ = -2102-4·7·(-3600)
Δ = 144900
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:

$\sqrt{\Delta}=\sqrt{144900}=\sqrt{900*161}=\sqrt{900}*\sqrt{161}=30\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-30\sqrt{161}}{2*7}=\frac{210-30\sqrt{161}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+30\sqrt{161}}{2*7}=\frac{210+30\sqrt{161}}{14}
$