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(3/2)x-4=13
We move all terms to the left:
(3/2)x-4-(13)=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-4-13=0
We add all the numbers together, and all the variables
(+3/2)x-17=0
We multiply parentheses
3x^2-17=0
a = 3; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·3·(-17)
Δ = 204
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{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{51}}{2*3}=\frac{0-2\sqrt{51}}{6} =-\frac{2\sqrt{51}}{6} =-\frac{\sqrt{51}}{3}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{51}}{2*3}=\frac{0+2\sqrt{51}}{6} =\frac{2\sqrt{51}}{6} =\frac{\sqrt{51}}{3}
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