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2x-10=1/2x+2
We move all terms to the left:
2x-10-(1/2x+2)=0
Domain of the equation: 2x+2)!=0We get rid of parentheses
x∈R
2x-1/2x-2-10=0
We multiply all the terms by the denominator
2x*2x-2*2x-10*2x-1=0
Wy multiply elements
4x^2-4x-20x-1=0
We add all the numbers together, and all the variables
4x^2-24x-1=0
a = 4; b = -24; c = -1;
Δ = b2-4ac
Δ = -242-4·4·(-1)
Δ = 592
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{37}}{2*4}=\frac{24-4\sqrt{37}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{37}}{2*4}=\frac{24+4\sqrt{37}}{8} $
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