5t^2+2t-49=0

Solution for 5t^2+2t-49=0 equation:

5t^2+2t-49=0

a = 5; b = 2; c = -49;
Δ = b2-4ac
Δ = 22-4·5·(-49)
Δ = 984
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:

$\sqrt{\Delta}=\sqrt{984}=\sqrt{4*246}=\sqrt{4}*\sqrt{246}=2\sqrt{246}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{246}}{2*5}=\frac{-2-2\sqrt{246}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{246}}{2*5}=\frac{-2+2\sqrt{246}}{10}
$