4t^2-3t-5=3.2

Solution for 4t^2-3t-5=3.2 equation:

4t^2-3t-5=3.2

We move all terms to the left:

4t^2-3t-5-(3.2)=0

We add all the numbers together, and all the variables

4t^2-3t-8.2=0

a = 4; b = -3; c = -8.2;
Δ = b2-4ac
Δ = -32-4·4·(-8.2)
Δ = 140.2
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{-(-3)-\sqrt{140.2}}{2*4}=\frac{3-\sqrt{140.2}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{140.2}}{2*4}=\frac{3+\sqrt{140.2}}{8}
$