Y=13x^2-18

Solution for Y=13x^2-18 equation:

=13Y^2-18

We move all terms to the left:

-(13Y^2-18)=0

We get rid of parentheses

-13Y^2+18=0

a = -13; b = 0; c = +18;
Δ = b2-4ac
Δ = 02-4·(-13)·18
Δ = 936
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:

$\sqrt{\Delta}=\sqrt{936}=\sqrt{36*26}=\sqrt{36}*\sqrt{26}=6\sqrt{26}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{26}}{2*-13}=\frac{0-6\sqrt{26}}{-26}
=-\frac{6\sqrt{26}}{-26}
=-\frac{3\sqrt{26}}{-13}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{26}}{2*-13}=\frac{0+6\sqrt{26}}{-26}
=\frac{6\sqrt{26}}{-26}
=\frac{3\sqrt{26}}{-13}
$