x+2x+(x-2)+1/4(2x)=63

Solution for x+2x+(x-2)+1/4(2x)=63 equation:

x+2x+(x-2)+1/4(2x)=63

We move all terms to the left:

x+2x+(x-2)+1/4(2x)-(63)=0


Domain of the equation: 42x!=0

x!=0/42

x!=0

x∈R


We add all the numbers together, and all the variables

3x+(x-2)+1/42x-63=0

We get rid of parentheses

3x+x+1/42x-2-63=0

We multiply all the terms by the denominator


3x*42x+x*42x-2*42x-63*42x+1=0

Wy multiply elements

126x^2+42x^2-84x-2646x+1=0

We add all the numbers together, and all the variables

168x^2-2730x+1=0

a = 168; b = -2730; c = +1;
Δ = b2-4ac
Δ = -27302-4·168·1
Δ = 7452228
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:

$\sqrt{\Delta}=\sqrt{7452228}=\sqrt{4*1863057}=\sqrt{4}*\sqrt{1863057}=2\sqrt{1863057}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2730)-2\sqrt{1863057}}{2*168}=\frac{2730-2\sqrt{1863057}}{336}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2730)+2\sqrt{1863057}}{2*168}=\frac{2730+2\sqrt{1863057}}{336}
$