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1/2x+17=4x+2
We move all terms to the left:
1/2x+17-(4x+2)=0
Domain of the equation: 2x!=0We get rid of parentheses
x!=0/2
x!=0
x∈R
1/2x-4x-2+17=0
We multiply all the terms by the denominator
-4x*2x-2*2x+17*2x+1=0
Wy multiply elements
-8x^2-4x+34x+1=0
We add all the numbers together, and all the variables
-8x^2+30x+1=0
a = -8; b = 30; c = +1;
Δ = b2-4ac
Δ = 302-4·(-8)·1
Δ = 932
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{932}=\sqrt{4*233}=\sqrt{4}*\sqrt{233}=2\sqrt{233}x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{233}}{2*-8}=\frac{-30-2\sqrt{233}}{-16}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{233}}{2*-8}=\frac{-30+2\sqrt{233}}{-16}
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