x-5/9x-136=0

Solution for x-5/9x-136=0 equation:

x-5/9x-136=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We multiply all the terms by the denominator


x*9x-136*9x-5=0

Wy multiply elements

9x^2-1224x-5=0

a = 9; b = -1224; c = -5;
Δ = b2-4ac
Δ = -12242-4·9·(-5)
Δ = 1498356
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:

$\sqrt{\Delta}=\sqrt{1498356}=\sqrt{36*41621}=\sqrt{36}*\sqrt{41621}=6\sqrt{41621}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1224)-6\sqrt{41621}}{2*9}=\frac{1224-6\sqrt{41621}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1224)+6\sqrt{41621}}{2*9}=\frac{1224+6\sqrt{41621}}{18}
$