-1/4x+6=2/2x+28

Solution for -1/4x+6=2/2x+28 equation:

-1/4x+6=2/2x+28

We move all terms to the left:

-1/4x+6-(2/2x+28)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x+28)!=0

x∈R


We get rid of parentheses

-1/4x-2/2x-28+6=0

We calculate fractions


(-2x)/8x^2+(-8x)/8x^2-28+6=0

We add all the numbers together, and all the variables

(-2x)/8x^2+(-8x)/8x^2-22=0

We multiply all the terms by the denominator


(-2x)+(-8x)-22*8x^2=0

Wy multiply elements

-176x^2+(-2x)+(-8x)=0

We get rid of parentheses

-176x^2-2x-8x=0

We add all the numbers together, and all the variables

-176x^2-10x=0

a = -176; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-176)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-176}=\frac{0}{-352}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-176}=\frac{20}{-352}
=-5/88
$