x-13=(-30)/x

Solution for x-13=(-30)/x equation:

x-13=(-30)/x

We move all terms to the left:

x-13-((-30)/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


x*x)-((-30)-13*x)=0

Wy multiply elements

x^2-13x=0

a = 1; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·1·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*1}=\frac{26}{2}
=13
$