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2x+5=-1/2x+10
We move all terms to the left:
2x+5-(-1/2x+10)=0
Domain of the equation: 2x+10)!=0We get rid of parentheses
x∈R
2x+1/2x-10+5=0
We multiply all the terms by the denominator
2x*2x-10*2x+5*2x+1=0
Wy multiply elements
4x^2-20x+10x+1=0
We add all the numbers together, and all the variables
4x^2-10x+1=0
a = 4; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·4·1
Δ = 84
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{21}}{2*4}=\frac{10-2\sqrt{21}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{21}}{2*4}=\frac{10+2\sqrt{21}}{8} $
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