t(t-6)=40

Solution for t(t-6)=40 equation:

t(t-6)=40

We move all terms to the left:

t(t-6)-(40)=0

We multiply parentheses

t^2-6t-40=0

a = 1; b = -6; c = -40;
Δ = b2-4ac
Δ = -62-4·1·(-40)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-14}{2*1}=\frac{-8}{2}
=-4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+14}{2*1}=\frac{20}{2}
=10
$