5/9x-4=2+x-18

Solution for 5/9x-4=2+x-18 equation:

5/9x-4=2+x-18

We move all terms to the left:

5/9x-4-(2+x-18)=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-(x-16)-4=0

We get rid of parentheses

5/9x-x+16-4=0

We multiply all the terms by the denominator


-x*9x+16*9x-4*9x+5=0

Wy multiply elements

-9x^2+144x-36x+5=0

We add all the numbers together, and all the variables

-9x^2+108x+5=0

a = -9; b = 108; c = +5;
Δ = b2-4ac
Δ = 1082-4·(-9)·5
Δ = 11844
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:

$\sqrt{\Delta}=\sqrt{11844}=\sqrt{36*329}=\sqrt{36}*\sqrt{329}=6\sqrt{329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-6\sqrt{329}}{2*-9}=\frac{-108-6\sqrt{329}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+6\sqrt{329}}{2*-9}=\frac{-108+6\sqrt{329}}{-18}
$