10u^2-5u-14=0

Solution for 10u^2-5u-14=0 equation:

10u^2-5u-14=0

a = 10; b = -5; c = -14;
Δ = b2-4ac
Δ = -52-4·10·(-14)
Δ = 585
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{65}}{2*10}=\frac{5-3\sqrt{65}}{20}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{65}}{2*10}=\frac{5+3\sqrt{65}}{20}
$