3/4x+2x-2=-1/4x+16

Solution for 3/4x+2x-2=-1/4x+16 equation:

3/4x+2x-2=-1/4x+16

We move all terms to the left:

3/4x+2x-2-(-1/4x+16)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 4x+16)!=0

x∈R


We add all the numbers together, and all the variables

2x+3/4x-(-1/4x+16)-2=0

We get rid of parentheses

2x+3/4x+1/4x-16-2=0

We multiply all the terms by the denominator


2x*4x-16*4x-2*4x+3+1=0

We add all the numbers together, and all the variables

2x*4x-16*4x-2*4x+4=0

Wy multiply elements

8x^2-64x-8x+4=0

We add all the numbers together, and all the variables

8x^2-72x+4=0

a = 8; b = -72; c = +4;
Δ = b2-4ac
Δ = -722-4·8·4
Δ = 5056
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:

$\sqrt{\Delta}=\sqrt{5056}=\sqrt{64*79}=\sqrt{64}*\sqrt{79}=8\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{79}}{2*8}=\frac{72-8\sqrt{79}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{79}}{2*8}=\frac{72+8\sqrt{79}}{16}
$