-3/4x-5/6=-1/2x

Solution for -3/4x-5/6=-1/2x equation:

-3/4x-5/6=-1/2x

We move all terms to the left:

-3/4x-5/6-(-1/2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-3/4x+1/2x-5/6=0

We calculate fractions


(-80x^2)/288x^2+(-216x)/288x^2+144x/288x^2=0

We multiply all the terms by the denominator


(-80x^2)+(-216x)+144x=0

We add all the numbers together, and all the variables

(-80x^2)+144x+(-216x)=0

We get rid of parentheses

-80x^2+144x-216x=0

We add all the numbers together, and all the variables

-80x^2-72x=0

a = -80; b = -72; c = 0;
Δ = b2-4ac
Δ = -722-4·(-80)·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-72}{2*-80}=\frac{0}{-160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+72}{2*-80}=\frac{144}{-160}
=-9/10
$