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7/12y-3=24y-20
We move all terms to the left:
7/12y-3-(24y-20)=0
Domain of the equation: 12y!=0We get rid of parentheses
y!=0/12
y!=0
y∈R
7/12y-24y+20-3=0
We multiply all the terms by the denominator
-24y*12y+20*12y-3*12y+7=0
Wy multiply elements
-288y^2+240y-36y+7=0
We add all the numbers together, and all the variables
-288y^2+204y+7=0
a = -288; b = 204; c = +7;
Δ = b2-4ac
Δ = 2042-4·(-288)·7
Δ = 49680
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{49680}=\sqrt{144*345}=\sqrt{144}*\sqrt{345}=12\sqrt{345}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(204)-12\sqrt{345}}{2*-288}=\frac{-204-12\sqrt{345}}{-576} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(204)+12\sqrt{345}}{2*-288}=\frac{-204+12\sqrt{345}}{-576} $
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