x-30/x=7

Solution for x-30/x=7 equation:

x-30/x=7

We move all terms to the left:

x-30/x-(7)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-7*x-30=0

We add all the numbers together, and all the variables

-7x+x*x-30=0

Wy multiply elements

x^2-7x-30=0

a = 1; b = -7; c = -30;
Δ = b2-4ac
Δ = -72-4·1·(-30)
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{-(-7)-13}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*1}=\frac{20}{2}
=10
$