-3/2x+3/4x=-9/10

Solution for -3/2x+3/4x=-9/10 equation:

-3/2x+3/4x=-9/10

We move all terms to the left:

-3/2x+3/4x-(-9/10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

-3/2x+3/4x+9/10=0

We calculate fractions


288x^2/80x^2+(-120x)/80x^2+60x/80x^2=0

We multiply all the terms by the denominator


288x^2+(-120x)+60x=0

We add all the numbers together, and all the variables

288x^2+60x+(-120x)=0

We get rid of parentheses

288x^2+60x-120x=0

We add all the numbers together, and all the variables

288x^2-60x=0

a = 288; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·288·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*288}=\frac{0}{576}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*288}=\frac{120}{576}
=5/24
$