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2/3y-16-5y=-12
We move all terms to the left:
2/3y-16-5y-(-12)=0
Domain of the equation: 3y!=0We add all the numbers together, and all the variables
y!=0/3
y!=0
y∈R
-5y+2/3y-4=0
We multiply all the terms by the denominator
-5y*3y-4*3y+2=0
Wy multiply elements
-15y^2-12y+2=0
a = -15; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·(-15)·2
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{-(-12)-2\sqrt{66}}{2*-15}=\frac{12-2\sqrt{66}}{-30} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{66}}{2*-15}=\frac{12+2\sqrt{66}}{-30} $
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