9/4x+6=15/2x-18

Solution for 9/4x+6=15/2x-18 equation:

9/4x+6=15/2x-18

We move all terms to the left:

9/4x+6-(15/2x-18)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x-18)!=0

x∈R


We get rid of parentheses

9/4x-15/2x+18+6=0

We calculate fractions


18x/8x^2+(-60x)/8x^2+18+6=0

We add all the numbers together, and all the variables

18x/8x^2+(-60x)/8x^2+24=0

We multiply all the terms by the denominator


18x+(-60x)+24*8x^2=0

Wy multiply elements

192x^2+18x+(-60x)=0

We get rid of parentheses

192x^2+18x-60x=0

We add all the numbers together, and all the variables

192x^2-42x=0

a = 192; b = -42; c = 0;
Δ = b2-4ac
Δ = -422-4·192·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-42}{2*192}=\frac{0}{384}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+42}{2*192}=\frac{84}{384}
=7/32
$