36y+12y^2=3/4

Solution for 36y+12y^2=3/4 equation:

36y+12y^2=3/4

We move all terms to the left:

36y+12y^2-(3/4)=0

We add all the numbers together, and all the variables

12y^2+36y-(+3/4)=0

We get rid of parentheses

12y^2+36y-3/4=0

We multiply all the terms by the denominator


12y^2*4+36y*4-3=0

Wy multiply elements

48y^2+144y-3=0

a = 48; b = 144; c = -3;
Δ = b2-4ac
Δ = 1442-4·48·(-3)
Δ = 21312
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:

$\sqrt{\Delta}=\sqrt{21312}=\sqrt{576*37}=\sqrt{576}*\sqrt{37}=24\sqrt{37}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-24\sqrt{37}}{2*48}=\frac{-144-24\sqrt{37}}{96}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+24\sqrt{37}}{2*48}=\frac{-144+24\sqrt{37}}{96}
$