2t^2+5t=8

Solution for 2t^2+5t=8 equation:

2t^2+5t=8

We move all terms to the left:

2t^2+5t-(8)=0

a = 2; b = 5; c = -8;
Δ = b2-4ac
Δ = 52-4·2·(-8)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{89}}{2*2}=\frac{-5-\sqrt{89}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{89}}{2*2}=\frac{-5+\sqrt{89}}{4}
$