2/4x+3x-7=21

Solution for 2/4x+3x-7=21 equation:

2/4x+3x-7=21

We move all terms to the left:

2/4x+3x-7-(21)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3x+2/4x-28=0

We multiply all the terms by the denominator


3x*4x-28*4x+2=0

Wy multiply elements

12x^2-112x+2=0

a = 12; b = -112; c = +2;
Δ = b2-4ac
Δ = -1122-4·12·2
Δ = 12448
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:

$\sqrt{\Delta}=\sqrt{12448}=\sqrt{16*778}=\sqrt{16}*\sqrt{778}=4\sqrt{778}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-4\sqrt{778}}{2*12}=\frac{112-4\sqrt{778}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+4\sqrt{778}}{2*12}=\frac{112+4\sqrt{778}}{24}
$