x+5+2x-8=1/4x+20

Solution for x+5+2x-8=1/4x+20 equation:

x+5+2x-8=1/4x+20

We move all terms to the left:

x+5+2x-8-(1/4x+20)=0


Domain of the equation: 4x+20)!=0

x∈R


We add all the numbers together, and all the variables

3x-(1/4x+20)-3=0

We get rid of parentheses

3x-1/4x-20-3=0

We multiply all the terms by the denominator


3x*4x-20*4x-3*4x-1=0

Wy multiply elements

12x^2-80x-12x-1=0

We add all the numbers together, and all the variables

12x^2-92x-1=0

a = 12; b = -92; c = -1;
Δ = b2-4ac
Δ = -922-4·12·(-1)
Δ = 8512
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:

$\sqrt{\Delta}=\sqrt{8512}=\sqrt{64*133}=\sqrt{64}*\sqrt{133}=8\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-8\sqrt{133}}{2*12}=\frac{92-8\sqrt{133}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+8\sqrt{133}}{2*12}=\frac{92+8\sqrt{133}}{24}
$