-5/4x+3/4=-2/3x-7

Solution for -5/4x+3/4=-2/3x-7 equation:

-5/4x+3/4=-2/3x-7

We move all terms to the left:

-5/4x+3/4-(-2/3x-7)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x-7)!=0

x∈R


We get rid of parentheses

-5/4x+2/3x+7+3/4=0

We calculate fractions


(-15x)/192x^2+128x/192x^2+9x/192x^2+7=0

We multiply all the terms by the denominator


(-15x)+128x+9x+7*192x^2=0

We add all the numbers together, and all the variables

137x+(-15x)+7*192x^2=0

Wy multiply elements

1344x^2+137x+(-15x)=0

We get rid of parentheses

1344x^2+137x-15x=0

We add all the numbers together, and all the variables

1344x^2+122x=0

a = 1344; b = 122; c = 0;
Δ = b2-4ac
Δ = 1222-4·1344·0
Δ = 14884
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14884}=122$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(122)-122}{2*1344}=\frac{-244}{2688}
=-61/672
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(122)+122}{2*1344}=\frac{0}{2688}
=0
$