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X+1/2X=70
We move all terms to the left:
X+1/2X-(70)=0
Domain of the equation: 2X!=0We multiply all the terms by the denominator
X!=0/2
X!=0
X∈R
X*2X-70*2X+1=0
Wy multiply elements
2X^2-140X+1=0
a = 2; b = -140; c = +1;
Δ = b2-4ac
Δ = -1402-4·2·1
Δ = 19592
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{19592}=\sqrt{4*4898}=\sqrt{4}*\sqrt{4898}=2\sqrt{4898}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-2\sqrt{4898}}{2*2}=\frac{140-2\sqrt{4898}}{4} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+2\sqrt{4898}}{2*2}=\frac{140+2\sqrt{4898}}{4} $
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