45=5t^2+2

Solution for 45=5t^2+2 equation:

45=5t^2+2

We move all terms to the left:

45-(5t^2+2)=0

We get rid of parentheses

-5t^2-2+45=0

We add all the numbers together, and all the variables

-5t^2+43=0

a = -5; b = 0; c = +43;
Δ = b2-4ac
Δ = 02-4·(-5)·43
Δ = 860
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{860}=\sqrt{4*215}=\sqrt{4}*\sqrt{215}=2\sqrt{215}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{215}}{2*-5}=\frac{0-2\sqrt{215}}{-10}
=-\frac{2\sqrt{215}}{-10}
=-\frac{\sqrt{215}}{-5}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{215}}{2*-5}=\frac{0+2\sqrt{215}}{-10}
=\frac{2\sqrt{215}}{-10}
=\frac{\sqrt{215}}{-5}
$