3.5t^2-13t-120=0

Solution for 3.5t^2-13t-120=0 equation:

3.5t^2-13t-120=0

a = 3.5; b = -13; c = -120;
Δ = b2-4ac
Δ = -132-4·3.5·(-120)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-43}{2*3.5}=\frac{-30}{7}
=-4+2/7
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+43}{2*3.5}=\frac{56}{7}
=8
$