-1/4x+7=-1/2x+31

Solution for -1/4x+7=-1/2x+31 equation:

-1/4x+7=-1/2x+31

We move all terms to the left:

-1/4x+7-(-1/2x+31)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x+31)!=0

x∈R


We get rid of parentheses

-1/4x+1/2x-31+7=0

We calculate fractions


(-2x)/8x^2+4x/8x^2-31+7=0

We add all the numbers together, and all the variables

(-2x)/8x^2+4x/8x^2-24=0

We multiply all the terms by the denominator


(-2x)+4x-24*8x^2=0

We add all the numbers together, and all the variables

4x+(-2x)-24*8x^2=0

Wy multiply elements

-192x^2+4x+(-2x)=0

We get rid of parentheses

-192x^2+4x-2x=0

We add all the numbers together, and all the variables

-192x^2+2x=0

a = -192; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-192)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-192}=\frac{-4}{-384}
=1/96
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-192}=\frac{0}{-384}
=0
$