7/12y-3=24y-20

Solution for 7/12y-3=24y-20 equation:

7/12y-3=24y-20

We move all terms to the left:

7/12y-3-(24y-20)=0


Domain of the equation: 12y!=0

y!=0/12

y!=0

y∈R


We get rid of parentheses

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}
$