5t^2=50t-5t^2

Solution for 5t^2=50t-5t^2 equation:

5t^2=50t-5t^2

We move all terms to the left:

5t^2-(50t-5t^2)=0

We get rid of parentheses

5t^2+5t^2-50t=0

We add all the numbers together, and all the variables

10t^2-50t=0

a = 10; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·10·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*10}=\frac{0}{20}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*10}=\frac{100}{20}
=5
$