5t2-4t=2

Solution for 5t2-4t=2 equation:

5t^2-4t=2

We move all terms to the left:

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

a = 5; b = -4; c = -2;
Δ = b2-4ac
Δ = -42-4·5·(-2)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{14}}{2*5}=\frac{4-2\sqrt{14}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{14}}{2*5}=\frac{4+2\sqrt{14}}{10}
$