4.9t^2-12.5t=75

Solution for 4.9t^2-12.5t=75 equation:

4.9t^2-12.5t=75

We move all terms to the left:

4.9t^2-12.5t-(75)=0

a = 4.9; b = -12.5; c = -75;
Δ = b2-4ac
Δ = -12.52-4·4.9·(-75)
Δ = 1626.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12.5)-\sqrt{1626.25}}{2*4.9}=\frac{12.5-\sqrt{1626.25}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12.5)+\sqrt{1626.25}}{2*4.9}=\frac{12.5+\sqrt{1626.25}}{9.8}
$