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X+1/2x+x-20=180

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Solution for X+1/2x+x-20=180 equation:



X+1/2X+X-20=180
We move all terms to the left:
X+1/2X+X-20-(180)=0
Domain of the equation: 2X!=0
X!=0/2
X!=0
X∈R
We add all the numbers together, and all the variables
2X+1/2X-200=0
We multiply all the terms by the denominator
2X*2X-200*2X+1=0
Wy multiply elements
4X^2-400X+1=0
a = 4; b = -400; c = +1;
Δ = b2-4ac
Δ = -4002-4·4·1
Δ = 159984
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{159984}=\sqrt{144*1111}=\sqrt{144}*\sqrt{1111}=12\sqrt{1111}
X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-12\sqrt{1111}}{2*4}=\frac{400-12\sqrt{1111}}{8}
X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+12\sqrt{1111}}{2*4}=\frac{400+12\sqrt{1111}}{8}

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