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

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

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

We move all terms to the left:

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


Domain of the equation: 2x+5)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

9x-4/2x-5=0

We multiply all the terms by the denominator


9x*2x-5*2x-4=0

Wy multiply elements

18x^2-10x-4=0

a = 18; b = -10; c = -4;
Δ = b2-4ac
Δ = -102-4·18·(-4)
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{97}}{2*18}=\frac{10-2\sqrt{97}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{97}}{2*18}=\frac{10+2\sqrt{97}}{36}
$