5x^2/x=5

Solution for 5x^2/x=5 equation:

5x^2/x=5

We move all terms to the left:

5x^2/x-(5)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


5x^2-5*x=0

We add all the numbers together, and all the variables

5x^2-5x=0

a = 5; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·5·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*5}=\frac{10}{10}
=1
$