3-((5y^2)/4)=0,y

Solution for 3-((5y^2)/4)=0,y equation:

3-((5y^2)/4)=0.y

We move all terms to the left:

3-((5y^2)/4)-(0.y)=0

We add all the numbers together, and all the variables

-(5y^2/4)+3-0=0

We add all the numbers together, and all the variables

-(5y^2/4)+3=0

We get rid of parentheses

-5y^2/4+3=0

We multiply all the terms by the denominator


-5y^2+3*4=0

We add all the numbers together, and all the variables

-5y^2+12=0

a = -5; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-5)·12
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*-5}=\frac{0-4\sqrt{15}}{-10}
=-\frac{4\sqrt{15}}{-10}
=-\frac{2\sqrt{15}}{-5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*-5}=\frac{0+4\sqrt{15}}{-10}
=\frac{4\sqrt{15}}{-10}
=\frac{2\sqrt{15}}{-5}
$