1/2x+7/4=3+1/6x

Solution for 1/2x+7/4=3+1/6x equation:

1/2x+7/4=3+1/6x

We move all terms to the left:

1/2x+7/4-(3+1/6x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(1/6x+3)+7/4=0

We get rid of parentheses

1/2x-1/6x-3+7/4=0

We calculate fractions


504x^2/192x^2+96x/192x^2+(-32x)/192x^2-3=0

We multiply all the terms by the denominator


504x^2+96x+(-32x)-3*192x^2=0

Wy multiply elements

504x^2-576x^2+96x+(-32x)=0

We get rid of parentheses

504x^2-576x^2+96x-32x=0

We add all the numbers together, and all the variables

-72x^2+64x=0

a = -72; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·(-72)·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*-72}=\frac{-128}{-144}
=8/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*-72}=\frac{0}{-144}
=0
$