0=9x-7/8x-5

Solution for 0=9x-7/8x-5 equation:

0=9x-7/8x-5

We move all terms to the left:

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


Domain of the equation: 8x-5)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-9x+7/8x+5=0

We multiply all the terms by the denominator


-9x*8x+5*8x+7=0

Wy multiply elements

-72x^2+40x+7=0

a = -72; b = 40; c = +7;
Δ = b2-4ac
Δ = 402-4·(-72)·7
Δ = 3616
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:

$\sqrt{\Delta}=\sqrt{3616}=\sqrt{16*226}=\sqrt{16}*\sqrt{226}=4\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{226}}{2*-72}=\frac{-40-4\sqrt{226}}{-144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{226}}{2*-72}=\frac{-40+4\sqrt{226}}{-144}
$