3/4x+2x=-1/4x+21

Solution for 3/4x+2x=-1/4x+21 equation:

3/4x+2x=-1/4x+21

We move all terms to the left:

3/4x+2x-(-1/4x+21)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 4x+21)!=0

x∈R


We add all the numbers together, and all the variables

2x+3/4x-(-1/4x+21)=0

We get rid of parentheses

2x+3/4x+1/4x-21=0

We multiply all the terms by the denominator


2x*4x-21*4x+3+1=0

We add all the numbers together, and all the variables

2x*4x-21*4x+4=0

Wy multiply elements

8x^2-84x+4=0

a = 8; b = -84; c = +4;
Δ = b2-4ac
Δ = -842-4·8·4
Δ = 6928
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6928}=\sqrt{16*433}=\sqrt{16}*\sqrt{433}=4\sqrt{433}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{433}}{2*8}=\frac{84-4\sqrt{433}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{433}}{2*8}=\frac{84+4\sqrt{433}}{16}
$