10a^2-12a-14=0

Solution for 10a^2-12a-14=0 equation:

10a^2-12a-14=0

a = 10; b = -12; c = -14;
Δ = b2-4ac
Δ = -122-4·10·(-14)
Δ = 704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{11}}{2*10}=\frac{12-8\sqrt{11}}{20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{11}}{2*10}=\frac{12+8\sqrt{11}}{20}
$