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1/2x+5=2x+8
We move all terms to the left:
1/2x+5-(2x+8)=0
Domain of the equation: 2x!=0We get rid of parentheses
x!=0/2
x!=0
x∈R
1/2x-2x-8+5=0
We multiply all the terms by the denominator
-2x*2x-8*2x+5*2x+1=0
Wy multiply elements
-4x^2-16x+10x+1=0
We add all the numbers together, and all the variables
-4x^2-6x+1=0
a = -4; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·(-4)·1
Δ = 52
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{13}}{2*-4}=\frac{6-2\sqrt{13}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{13}}{2*-4}=\frac{6+2\sqrt{13}}{-8} $
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