9/7x+x=13

Solution for 9/7x+x=13 equation:

9/7x+x=13

We move all terms to the left:

9/7x+x-(13)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

x+9/7x-13=0

We multiply all the terms by the denominator


x*7x-13*7x+9=0

Wy multiply elements

7x^2-91x+9=0

a = 7; b = -91; c = +9;
Δ = b2-4ac
Δ = -912-4·7·9
Δ = 8029
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-91)-\sqrt{8029}}{2*7}=\frac{91-\sqrt{8029}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-91)+\sqrt{8029}}{2*7}=\frac{91+\sqrt{8029}}{14}
$