10t^2+8t^2=15^2

Solution for 10t^2+8t^2=15^2 equation:

10t^2+8t^2=15^2

We move all terms to the left:

10t^2+8t^2-(15^2)=0

We add all the numbers together, and all the variables

18t^2-225=0

a = 18; b = 0; c = -225;
Δ = b2-4ac
Δ = 02-4·18·(-225)
Δ = 16200
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:

$\sqrt{\Delta}=\sqrt{16200}=\sqrt{8100*2}=\sqrt{8100}*\sqrt{2}=90\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-90\sqrt{2}}{2*18}=\frac{0-90\sqrt{2}}{36}
=-\frac{90\sqrt{2}}{36}
=-\frac{5\sqrt{2}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+90\sqrt{2}}{2*18}=\frac{0+90\sqrt{2}}{36}
=\frac{90\sqrt{2}}{36}
=\frac{5\sqrt{2}}{2}
$