-7t^2=2+9t

Solution for -7t^2=2+9t equation:

-7t^2=2+9t

We move all terms to the left:

-7t^2-(2+9t)=0

We add all the numbers together, and all the variables

-7t^2-(9t+2)=0

We get rid of parentheses

-7t^2-9t-2=0

a = -7; b = -9; c = -2;
Δ = b2-4ac
Δ = -92-4·(-7)·(-2)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-5}{2*-7}=\frac{4}{-14}
=-2/7
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+5}{2*-7}=\frac{14}{-14}
=-1
$