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1/2x+8=2x-5
We move all terms to the left:
1/2x+8-(2x-5)=0
Domain of the equation: 2x!=0We get rid of parentheses
x!=0/2
x!=0
x∈R
1/2x-2x+5+8=0
We multiply all the terms by the denominator
-2x*2x+5*2x+8*2x+1=0
Wy multiply elements
-4x^2+10x+16x+1=0
We add all the numbers together, and all the variables
-4x^2+26x+1=0
a = -4; b = 26; c = +1;
Δ = b2-4ac
Δ = 262-4·(-4)·1
Δ = 692
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{692}=\sqrt{4*173}=\sqrt{4}*\sqrt{173}=2\sqrt{173}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{173}}{2*-4}=\frac{-26-2\sqrt{173}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{173}}{2*-4}=\frac{-26+2\sqrt{173}}{-8} $
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