5/9x+5=97-2x

Solution for 5/9x+5=97-2x equation:

5/9x+5=97-2x

We move all terms to the left:

5/9x+5-(97-2x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

5/9x-(-2x+97)+5=0

We get rid of parentheses

5/9x+2x-97+5=0

We multiply all the terms by the denominator


2x*9x-97*9x+5*9x+5=0

Wy multiply elements

18x^2-873x+45x+5=0

We add all the numbers together, and all the variables

18x^2-828x+5=0

a = 18; b = -828; c = +5;
Δ = b2-4ac
Δ = -8282-4·18·5
Δ = 685224
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:

$\sqrt{\Delta}=\sqrt{685224}=\sqrt{36*19034}=\sqrt{36}*\sqrt{19034}=6\sqrt{19034}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-828)-6\sqrt{19034}}{2*18}=\frac{828-6\sqrt{19034}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-828)+6\sqrt{19034}}{2*18}=\frac{828+6\sqrt{19034}}{36}
$