7x-5/9x+6=8

Solution for 7x-5/9x+6=8 equation:

7x-5/9x+6=8

We move all terms to the left:

7x-5/9x+6-(8)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

7x-5/9x-2=0

We multiply all the terms by the denominator


7x*9x-2*9x-5=0

Wy multiply elements

63x^2-18x-5=0

a = 63; b = -18; c = -5;
Δ = b2-4ac
Δ = -182-4·63·(-5)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-12\sqrt{11}}{2*63}=\frac{18-12\sqrt{11}}{126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+12\sqrt{11}}{2*63}=\frac{18+12\sqrt{11}}{126}
$