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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-7)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-4x)/8x^2+(-2x)/8x^2+7+7=0

We add all the numbers together, and all the variables

(-4x)/8x^2+(-2x)/8x^2+14=0

We multiply all the terms by the denominator


(-4x)+(-2x)+14*8x^2=0

Wy multiply elements

112x^2+(-4x)+(-2x)=0

We get rid of parentheses

112x^2-4x-2x=0

We add all the numbers together, and all the variables

112x^2-6x=0

a = 112; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·112·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*112}=\frac{0}{224}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*112}=\frac{12}{224}
=3/56
$