T=-5t2+40t-35

Solution for T=-5t2+40t-35 equation:

=-5T^2+40T-35

We move all terms to the left:

-(-5T^2+40T-35)=0

We get rid of parentheses

5T^2-40T+35=0

a = 5; b = -40; c = +35;
Δ = b2-4ac
Δ = -402-4·5·35
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-30}{2*5}=\frac{10}{10}
=1
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+30}{2*5}=\frac{70}{10}
=7
$