1/2x+5/4=-2/3x

Solution for 1/2x+5/4=-2/3x equation:

1/2x+5/4=-2/3x

We move all terms to the left:

1/2x+5/4-(-2/3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

1/2x+2/3x+5/4=0

We calculate fractions


90x^2/96x^2+48x/96x^2+64x/96x^2=0

We multiply all the terms by the denominator


90x^2+48x+64x=0

We add all the numbers together, and all the variables

90x^2+112x=0

a = 90; b = 112; c = 0;
Δ = b2-4ac
Δ = 1122-4·90·0
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-112}{2*90}=\frac{-224}{180}
=-1+11/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+112}{2*90}=\frac{0}{180}
=0
$