5t-6=-t^2

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

5t-6=-t^2

We move all terms to the left:

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

We get rid of parentheses

t^2+5t-6=0

a = 1; b = 5; c = -6;
Δ = b2-4ac
Δ = 52-4·1·(-6)
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{-(5)-7}{2*1}=\frac{-12}{2}
=-6
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*1}=\frac{2}{2}
=1
$