2.5t^2=0.75t^2+25

Solution for 2.5t^2=0.75t^2+25 equation:

2.5t^2=0.75t^2+25

We move all terms to the left:

2.5t^2-(0.75t^2+25)=0

We get rid of parentheses

2.5t^2-0.75t^2-25=0

We add all the numbers together, and all the variables

1.75t^2-25=0

a = 1.75; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·1.75·(-25)
Δ = 175
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:

$\sqrt{\Delta}=\sqrt{175}=\sqrt{25*7}=\sqrt{25}*\sqrt{7}=5\sqrt{7}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-5\sqrt{7}}{2*1.75}=\frac{0-5\sqrt{7}}{3.5}
=-\frac{5\sqrt{7}}{3.5}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+5\sqrt{7}}{2*1.75}=\frac{0+5\sqrt{7}}{3.5}
=\frac{5\sqrt{7}}{3.5}
$