x+7/6x+9/6x=88

Solution for x+7/6x+9/6x=88 equation:

x+7/6x+9/6x=88

We move all terms to the left:

x+7/6x+9/6x-(88)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


x*6x-88*6x+7+9=0

We add all the numbers together, and all the variables

x*6x-88*6x+16=0

Wy multiply elements

6x^2-528x+16=0

a = 6; b = -528; c = +16;
Δ = b2-4ac
Δ = -5282-4·6·16
Δ = 278400
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:

$\sqrt{\Delta}=\sqrt{278400}=\sqrt{1600*174}=\sqrt{1600}*\sqrt{174}=40\sqrt{174}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-528)-40\sqrt{174}}{2*6}=\frac{528-40\sqrt{174}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-528)+40\sqrt{174}}{2*6}=\frac{528+40\sqrt{174}}{12}
$