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(3/2)y+7=29
We move all terms to the left:
(3/2)y+7-(29)=0
Domain of the equation: 2)y!=0We add all the numbers together, and all the variables
y!=0/1
y!=0
y∈R
(+3/2)y+7-29=0
We add all the numbers together, and all the variables
(+3/2)y-22=0
We multiply parentheses
3y^2-22=0
a = 3; b = 0; c = -22;
Δ = b2-4ac
Δ = 02-4·3·(-22)
Δ = 264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{66}}{2*3}=\frac{0-2\sqrt{66}}{6} =-\frac{2\sqrt{66}}{6} =-\frac{\sqrt{66}}{3} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{66}}{2*3}=\frac{0+2\sqrt{66}}{6} =\frac{2\sqrt{66}}{6} =\frac{\sqrt{66}}{3} $
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