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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


18x^2/96x^2+(-336x)/96x^2+(-32x)/96x^2+2=0

We multiply all the terms by the denominator


18x^2+(-336x)+(-32x)+2*96x^2=0

Wy multiply elements

18x^2+192x^2+(-336x)+(-32x)=0

We get rid of parentheses

18x^2+192x^2-336x-32x=0

We add all the numbers together, and all the variables

210x^2-368x=0

a = 210; b = -368; c = 0;
Δ = b2-4ac
Δ = -3682-4·210·0
Δ = 135424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{135424}=368$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-368)-368}{2*210}=\frac{0}{420}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-368)+368}{2*210}=\frac{736}{420}
=1+79/105
$