2t^2+9t=35

Solution for 2t^2+9t=35 equation:

2t^2+9t=35

We move all terms to the left:

2t^2+9t-(35)=0

a = 2; b = 9; c = -35;
Δ = b2-4ac
Δ = 92-4·2·(-35)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-19}{2*2}=\frac{-28}{4}
=-7
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+19}{2*2}=\frac{10}{4}
=2+1/2
$