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(3/2)x=24
We move all terms to the left:
(3/2)x-(24)=0
Domain of the equation: 2)x!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
(+3/2)x-24=0
We multiply parentheses
3x^2-24=0
a = 3; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·3·(-24)
Δ = 288
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*3}=\frac{0-12\sqrt{2}}{6} =-\frac{12\sqrt{2}}{6} =-2\sqrt{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*3}=\frac{0+12\sqrt{2}}{6} =\frac{12\sqrt{2}}{6} =2\sqrt{2} $
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