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0.5x+8=2/3x
We move all terms to the left:
0.5x+8-(2/3x)=0
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
0.5x-(+2/3x)+8=0
We get rid of parentheses
0.5x-2/3x+8=0
We multiply all the terms by the denominator
(0.5x)*3x+8*3x-2=0
We add all the numbers together, and all the variables
(+0.5x)*3x+8*3x-2=0
We multiply parentheses
0x^2+8*3x-2=0
Wy multiply elements
0x^2+24x-2=0
We add all the numbers together, and all the variables
x^2+24x-2=0
a = 1; b = 24; c = -2;
Δ = b2-4ac
Δ = 242-4·1·(-2)
Δ = 584
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{584}=\sqrt{4*146}=\sqrt{4}*\sqrt{146}=2\sqrt{146}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{146}}{2*1}=\frac{-24-2\sqrt{146}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{146}}{2*1}=\frac{-24+2\sqrt{146}}{2} $
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