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1/2x+x+14=59
We move all terms to the left:
1/2x+x+14-(59)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
x+1/2x-45=0
We multiply all the terms by the denominator
x*2x-45*2x+1=0
Wy multiply elements
2x^2-90x+1=0
a = 2; b = -90; c = +1;
Δ = b2-4ac
Δ = -902-4·2·1
Δ = 8092
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8092}=\sqrt{1156*7}=\sqrt{1156}*\sqrt{7}=34\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-34\sqrt{7}}{2*2}=\frac{90-34\sqrt{7}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+34\sqrt{7}}{2*2}=\frac{90+34\sqrt{7}}{4} $
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