Y=6.5y^2-8

Solution for Y=6.5y^2-8 equation:

=6.5Y^2-8

We move all terms to the left:

-(6.5Y^2-8)=0

We get rid of parentheses

-6.5Y^2+8=0

a = -6.5; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-6.5)·8
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{13}}{2*-6.5}=\frac{0-4\sqrt{13}}{-13}
=-\frac{4\sqrt{13}}{-13}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{13}}{2*-6.5}=\frac{0+4\sqrt{13}}{-13}
=\frac{4\sqrt{13}}{-13}
$