(50t)2+(60t)2=3002

Solution for (50t)2+(60t)2=3002 equation:

(50t)2+(60t)2=3002

We move all terms to the left:

(50t)2+(60t)2-(3002)=0

We add all the numbers together, and all the variables

110t^2-3002=0

a = 110; b = 0; c = -3002;
Δ = b2-4ac
Δ = 02-4·110·(-3002)
Δ = 1320880
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:

$\sqrt{\Delta}=\sqrt{1320880}=\sqrt{16*82555}=\sqrt{16}*\sqrt{82555}=4\sqrt{82555}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{82555}}{2*110}=\frac{0-4\sqrt{82555}}{220}
=-\frac{4\sqrt{82555}}{220}
=-\frac{\sqrt{82555}}{55}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{82555}}{2*110}=\frac{0+4\sqrt{82555}}{220}
=\frac{4\sqrt{82555}}{220}
=\frac{\sqrt{82555}}{55}
$