2.25y-12=1/4y-4

Solution for 2.25y-12=1/4y-4 equation:

2.25y-12=1/4y-4

We move all terms to the left:

2.25y-12-(1/4y-4)=0


Domain of the equation: 4y-4)!=0

y∈R


We get rid of parentheses

2.25y-1/4y+4-12=0

We multiply all the terms by the denominator


(2.25y)*4y+4*4y-12*4y-1=0

We add all the numbers together, and all the variables

(+2.25y)*4y+4*4y-12*4y-1=0

We multiply parentheses

8y^2+4*4y-12*4y-1=0

Wy multiply elements

8y^2+16y-48y-1=0

We add all the numbers together, and all the variables

8y^2-32y-1=0

a = 8; b = -32; c = -1;
Δ = b2-4ac
Δ = -322-4·8·(-1)
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{66}}{2*8}=\frac{32-4\sqrt{66}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{66}}{2*8}=\frac{32+4\sqrt{66}}{16}
$