y^2-3y=-1/4

Solution for y^2-3y=-1/4 equation:

y^2-3y=-1/4

We move all terms to the left:

y^2-3y-(-1/4)=0

We get rid of parentheses

y^2-3y+1/4=0

We multiply all the terms by the denominator


y^2*4-3y*4+1=0

Wy multiply elements

4y^2-12y+1=0

a = 4; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·4·1
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{2}}{2*4}=\frac{12-8\sqrt{2}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{2}}{2*4}=\frac{12+8\sqrt{2}}{8}
$