8-5t^2=4t

Solution for 8-5t^2=4t equation:

8-5t^2=4t

We move all terms to the left:

8-5t^2-(4t)=0

a = -5; b = -4; c = +8;
Δ = b2-4ac
Δ = -42-4·(-5)·8
Δ = 176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{11}}{2*-5}=\frac{4-4\sqrt{11}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{11}}{2*-5}=\frac{4+4\sqrt{11}}{-10}
$