9/4y-12=1.4y-4

Solution for 9/4y-12=1.4y-4 equation:

9/4y-12=1.4y-4

We move all terms to the left:

9/4y-12-(1.4y-4)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We get rid of parentheses

9/4y-1.4y+4-12=0

We multiply all the terms by the denominator


-(1.4y)*4y+4*4y-12*4y+9=0

We add all the numbers together, and all the variables

-(+1.4y)*4y+4*4y-12*4y+9=0

We multiply parentheses

-4y^2+4*4y-12*4y+9=0

Wy multiply elements

-4y^2+16y-48y+9=0

We add all the numbers together, and all the variables

-4y^2-32y+9=0

a = -4; b = -32; c = +9;
Δ = b2-4ac
Δ = -322-4·(-4)·9
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{73}}{2*-4}=\frac{32-4\sqrt{73}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{73}}{2*-4}=\frac{32+4\sqrt{73}}{-8}
$