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

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



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

We move all terms to the left:

X-42+2X-59+1/4X+21-(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}
$

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