5/1x+65=-1x+-7

Solution for 5/1x+65=-1x+-7 equation:

5/1x+65=-1x+-7

We move all terms to the left:

5/1x+65-(-1x+-7)=0


Domain of the equation: 1x!=0

x∈R


We add all the numbers together, and all the variables

5/1x-(-1x-7)+65=0

We get rid of parentheses

5/1x+1x+7+65=0

We multiply all the terms by the denominator


1x*1x+7*1x+65*1x+5=0

Wy multiply elements

x^2+7x+65x+5=0

We add all the numbers together, and all the variables

x^2+72x+5=0

a = 1; b = 72; c = +5;
Δ = b2-4ac
Δ = 722-4·1·5
Δ = 5164
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:

$\sqrt{\Delta}=\sqrt{5164}=\sqrt{4*1291}=\sqrt{4}*\sqrt{1291}=2\sqrt{1291}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-2\sqrt{1291}}{2*1}=\frac{-72-2\sqrt{1291}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+2\sqrt{1291}}{2*1}=\frac{-72+2\sqrt{1291}}{2}
$