Y=-3/4x2+7

Solution for Y=-3/4x2+7 equation:

=-3/4Y^2+7

We move all terms to the left:

-(-3/4Y^2+7)=0


Domain of the equation: 4Y^2+7)!=0

Y∈R


We get rid of parentheses

3/4Y^2-7=0

We multiply all the terms by the denominator


-7*4Y^2+3=0

Wy multiply elements

-28Y^2+3=0

a = -28; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-28)·3
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{21}}{2*-28}=\frac{0-4\sqrt{21}}{-56}
=-\frac{4\sqrt{21}}{-56}
=-\frac{\sqrt{21}}{-14}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{21}}{2*-28}=\frac{0+4\sqrt{21}}{-56}
=\frac{4\sqrt{21}}{-56}
=\frac{\sqrt{21}}{-14}
$