Y=5x^2-30+6

Solution for Y=5x^2-30+6 equation:

=5Y^2-30+6

We move all terms to the left:

-(5Y^2-30+6)=0

We get rid of parentheses

-5Y^2+30-6=0

We add all the numbers together, and all the variables

-5Y^2+24=0

a = -5; b = 0; c = +24;
Δ = b2-4ac
Δ = 02-4·(-5)·24
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*-5}=\frac{0-4\sqrt{30}}{-10}
=-\frac{4\sqrt{30}}{-10}
=-\frac{2\sqrt{30}}{-5}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*-5}=\frac{0+4\sqrt{30}}{-10}
=\frac{4\sqrt{30}}{-10}
=\frac{2\sqrt{30}}{-5}
$