2t^2+10t=50

Solution for 2t^2+10t=50 equation:

2t^2+10t=50

We move all terms to the left:

2t^2+10t-(50)=0

a = 2; b = 10; c = -50;
Δ = b2-4ac
Δ = 102-4·2·(-50)
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{5}}{2*2}=\frac{-10-10\sqrt{5}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{5}}{2*2}=\frac{-10+10\sqrt{5}}{4}
$