6=-5t^2+7t+6

Solution for 6=-5t^2+7t+6 equation:

6=-5t^2+7t+6

We move all terms to the left:

6-(-5t^2+7t+6)=0

We get rid of parentheses

5t^2-7t-6+6=0

We add all the numbers together, and all the variables

5t^2-7t=0

a = 5; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·5·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*5}=\frac{0}{10}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*5}=\frac{14}{10}
=1+2/5
$