9x-8/2x+5=8

Solution for 9x-8/2x+5=8 equation:

9x-8/2x+5=8

We move all terms to the left:

9x-8/2x+5-(8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

9x-8/2x-3=0

We multiply all the terms by the denominator


9x*2x-3*2x-8=0

Wy multiply elements

18x^2-6x-8=0

a = 18; b = -6; c = -8;
Δ = b2-4ac
Δ = -62-4·18·(-8)
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{17}}{2*18}=\frac{6-6\sqrt{17}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{17}}{2*18}=\frac{6+6\sqrt{17}}{36}
$