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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


64x/128x^2+6x/128x^2+2x/128x^2-4=0

We multiply all the terms by the denominator


64x+6x+2x-4*128x^2=0

We add all the numbers together, and all the variables

72x-4*128x^2=0

Wy multiply elements

-512x^2+72x=0

a = -512; b = 72; c = 0;
Δ = b2-4ac
Δ = 722-4·(-512)·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72}{2*-512}=\frac{-144}{-1024}
=9/64
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72}{2*-512}=\frac{0}{-1024}
=0
$