7/9x+2=5x-13

Solution for 7/9x+2=5x-13 equation:

7/9x+2=5x-13

We move all terms to the left:

7/9x+2-(5x-13)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We get rid of parentheses

7/9x-5x+13+2=0

We multiply all the terms by the denominator


-5x*9x+13*9x+2*9x+7=0

Wy multiply elements

-45x^2+117x+18x+7=0

We add all the numbers together, and all the variables

-45x^2+135x+7=0

a = -45; b = 135; c = +7;
Δ = b2-4ac
Δ = 1352-4·(-45)·7
Δ = 19485
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:

$\sqrt{\Delta}=\sqrt{19485}=\sqrt{9*2165}=\sqrt{9}*\sqrt{2165}=3\sqrt{2165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(135)-3\sqrt{2165}}{2*-45}=\frac{-135-3\sqrt{2165}}{-90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(135)+3\sqrt{2165}}{2*-45}=\frac{-135+3\sqrt{2165}}{-90}
$