Y=30(5^2t-1)

Solution for Y=30(5^2t-1) equation:

=30(5^2Y-1)

We move all terms to the left:

-(30(5^2Y-1))=0


We calculate terms in parentheses: -(30(5^2Y-1)), so:

30(5^2Y-1)

We multiply parentheses

150Y^2-30

Back to the equation:

-(150Y^2-30)


We get rid of parentheses

-150Y^2+30=0

a = -150; b = 0; c = +30;
Δ = b2-4ac
Δ = 02-4·(-150)·30
Δ = 18000
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:

$\sqrt{\Delta}=\sqrt{18000}=\sqrt{3600*5}=\sqrt{3600}*\sqrt{5}=60\sqrt{5}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{5}}{2*-150}=\frac{0-60\sqrt{5}}{-300}
=-\frac{60\sqrt{5}}{-300}
=-\frac{\sqrt{5}}{-5}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{5}}{2*-150}=\frac{0+60\sqrt{5}}{-300}
=\frac{60\sqrt{5}}{-300}
=\frac{\sqrt{5}}{-5}
$