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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


216x^2/192x^2+96x/192x^2+(-160x)/192x^2+2=0

We multiply all the terms by the denominator


216x^2+96x+(-160x)+2*192x^2=0

Wy multiply elements

216x^2+384x^2+96x+(-160x)=0

We get rid of parentheses

216x^2+384x^2+96x-160x=0

We add all the numbers together, and all the variables

600x^2-64x=0

a = 600; b = -64; c = 0;
Δ = b2-4ac
Δ = -642-4·600·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-64}{2*600}=\frac{0}{1200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+64}{2*600}=\frac{128}{1200}
=8/75
$