x^2/x-7=49/x-7

Solution for x^2/x-7=49/x-7 equation:

x^2/x-7=49/x-7

We move all terms to the left:

x^2/x-7-(49/x-7)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-7)!=0

x∈R


We get rid of parentheses

x^2/x-49/x+7-7=0

We multiply all the terms by the denominator


x^2+7*x-7*x-49=0

We add all the numbers together, and all the variables

x^2-49=0

a = 1; b = 0; c = -49;
Δ = b2-4ac
Δ = 02-4·1·(-49)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14}{2*1}=\frac{-14}{2}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14}{2*1}=\frac{14}{2}
=7
$