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2x-50+1/2x+15=90
We move all terms to the left:
2x-50+1/2x+15-(90)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
2x+1/2x-125=0
We multiply all the terms by the denominator
2x*2x-125*2x+1=0
Wy multiply elements
4x^2-250x+1=0
a = 4; b = -250; c = +1;
Δ = b2-4ac
Δ = -2502-4·4·1
Δ = 62484
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{62484}=\sqrt{4*15621}=\sqrt{4}*\sqrt{15621}=2\sqrt{15621}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-2\sqrt{15621}}{2*4}=\frac{250-2\sqrt{15621}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+2\sqrt{15621}}{2*4}=\frac{250+2\sqrt{15621}}{8} $
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