x-42+1/4x+21+2x-59=180

Solution for x-42+1/4x+21+2x-59=180 equation:

x-42+1/4x+21+2x-59=180

We move all terms to the left:

x-42+1/4x+21+2x-59-(180)=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+1/4x-260=0

We multiply all the terms by the denominator


3x*4x-260*4x+1=0

Wy multiply elements

12x^2-1040x+1=0

a = 12; b = -1040; c = +1;
Δ = b2-4ac
Δ = -10402-4·12·1
Δ = 1081552
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:

$\sqrt{\Delta}=\sqrt{1081552}=\sqrt{16*67597}=\sqrt{16}*\sqrt{67597}=4\sqrt{67597}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1040)-4\sqrt{67597}}{2*12}=\frac{1040-4\sqrt{67597}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1040)+4\sqrt{67597}}{2*12}=\frac{1040+4\sqrt{67597}}{24}
$