7x+5/x-3=26/x-3

Solution for 7x+5/x-3=26/x-3 equation:

7x+5/x-3=26/x-3

We move all terms to the left:

7x+5/x-3-(26/x-3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-3)!=0

x∈R


We get rid of parentheses

7x+5/x-26/x+3-3=0

We multiply all the terms by the denominator


7x*x+3*x-3*x+5-26=0

We add all the numbers together, and all the variables

7x*x-21=0

Wy multiply elements

7x^2-21=0

a = 7; b = 0; c = -21;
Δ = b2-4ac
Δ = 02-4·7·(-21)
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{3}}{2*7}=\frac{0-14\sqrt{3}}{14}
=-\frac{14\sqrt{3}}{14}
=-\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{3}}{2*7}=\frac{0+14\sqrt{3}}{14}
=\frac{14\sqrt{3}}{14}
=\sqrt{3}
$