3/4y^2-11=232

Solution for 3/4y^2-11=232 equation:

3/4y^2-11=232

We move all terms to the left:

3/4y^2-11-(232)=0


Domain of the equation: 4y^2!=0

y^2!=0/4

y^2!=√0

y!=0

y∈R


We add all the numbers together, and all the variables

3/4y^2-243=0

We multiply all the terms by the denominator


-243*4y^2+3=0

Wy multiply elements

-972y^2+3=0

a = -972; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-972)·3
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-108}{2*-972}=\frac{-108}{-1944}
=1/18
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+108}{2*-972}=\frac{108}{-1944}
=-1/18
$