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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

8x^2-84x-12x+2=0

We add all the numbers together, and all the variables

8x^2-96x+2=0

a = 8; b = -96; c = +2;
Δ = b2-4ac
Δ = -962-4·8·2
Δ = 9152
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:

$\sqrt{\Delta}=\sqrt{9152}=\sqrt{64*143}=\sqrt{64}*\sqrt{143}=8\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-8\sqrt{143}}{2*8}=\frac{96-8\sqrt{143}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+8\sqrt{143}}{2*8}=\frac{96+8\sqrt{143}}{16}
$