0=5x-7/9x+2

Solution for 0=5x-7/9x+2 equation:

0=5x-7/9x+2

We move all terms to the left:

0-(5x-7/9x+2)=0


Domain of the equation: 9x+2)!=0

x∈R


We add all the numbers together, and all the variables

-(5x-7/9x+2)=0

We get rid of parentheses

-5x+7/9x-2=0

We multiply all the terms by the denominator


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

Wy multiply elements

-45x^2-18x+7=0

a = -45; b = -18; c = +7;
Δ = b2-4ac
Δ = -182-4·(-45)·7
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*-45}=\frac{18-12\sqrt{11}}{-90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+12\sqrt{11}}{2*-45}=\frac{18+12\sqrt{11}}{-90}
$