5x+113=15/x+7

Solution for 5x+113=15/x+7 equation:

5x+113=15/x+7

We move all terms to the left:

5x+113-(15/x+7)=0


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

x∈R


We get rid of parentheses

5x-15/x-7+113=0

We multiply all the terms by the denominator


5x*x-7*x+113*x-15=0

We add all the numbers together, and all the variables

106x+5x*x-15=0

Wy multiply elements

5x^2+106x-15=0

a = 5; b = 106; c = -15;
Δ = b2-4ac
Δ = 1062-4·5·(-15)
Δ = 11536
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:

$\sqrt{\Delta}=\sqrt{11536}=\sqrt{16*721}=\sqrt{16}*\sqrt{721}=4\sqrt{721}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(106)-4\sqrt{721}}{2*5}=\frac{-106-4\sqrt{721}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(106)+4\sqrt{721}}{2*5}=\frac{-106+4\sqrt{721}}{10}
$