9/4y-12=14y-4

Solution for 9/4y-12=14y-4 equation:

9/4y-12=14y-4

We move all terms to the left:

9/4y-12-(14y-4)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We get rid of parentheses

9/4y-14y+4-12=0

We multiply all the terms by the denominator


-14y*4y+4*4y-12*4y+9=0

Wy multiply elements

-56y^2+16y-48y+9=0

We add all the numbers together, and all the variables

-56y^2-32y+9=0

a = -56; b = -32; c = +9;
Δ = b2-4ac
Δ = -322-4·(-56)·9
Δ = 3040
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:

$\sqrt{\Delta}=\sqrt{3040}=\sqrt{16*190}=\sqrt{16}*\sqrt{190}=4\sqrt{190}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{190}}{2*-56}=\frac{32-4\sqrt{190}}{-112}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{190}}{2*-56}=\frac{32+4\sqrt{190}}{-112}
$