1/2x+1=41/4x-6

Solution for 1/2x+1=41/4x-6 equation:

1/2x+1=41/4x-6

We move all terms to the left:

1/2x+1-(41/4x-6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-6)!=0

x∈R


We get rid of parentheses

1/2x-41/4x+6+1=0

We calculate fractions


4x/8x^2+(-82x)/8x^2+6+1=0

We add all the numbers together, and all the variables

4x/8x^2+(-82x)/8x^2+7=0

We multiply all the terms by the denominator


4x+(-82x)+7*8x^2=0

Wy multiply elements

56x^2+4x+(-82x)=0

We get rid of parentheses

56x^2+4x-82x=0

We add all the numbers together, and all the variables

56x^2-78x=0

a = 56; b = -78; c = 0;
Δ = b2-4ac
Δ = -782-4·56·0
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-78}{2*56}=\frac{0}{112}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+78}{2*56}=\frac{156}{112}
=1+11/28
$