3-4y^2=-193

Solution for 3-4y^2=-193 equation:

3-4y^2=-193

We move all terms to the left:

3-4y^2-(-193)=0

We add all the numbers together, and all the variables

-4y^2+196=0

a = -4; b = 0; c = +196;
Δ = b2-4ac
Δ = 02-4·(-4)·196
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-56}{2*-4}=\frac{-56}{-8}
=+7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+56}{2*-4}=\frac{56}{-8}
=-7
$