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(2/3)x-5=47
We move all terms to the left:
(2/3)x-5-(47)=0
Domain of the equation: 3)x!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
(+2/3)x-5-47=0
We add all the numbers together, and all the variables
(+2/3)x-52=0
We multiply parentheses
2x^2-52=0
a = 2; b = 0; c = -52;
Δ = b2-4ac
Δ = 02-4·2·(-52)
Δ = 416
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{26}}{2*2}=\frac{0-4\sqrt{26}}{4} =-\frac{4\sqrt{26}}{4} =-\sqrt{26} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{26}}{2*2}=\frac{0+4\sqrt{26}}{4} =\frac{4\sqrt{26}}{4} =\sqrt{26} $
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