10a^2-43a-17=0

Solution for 10a^2-43a-17=0 equation:

10a^2-43a-17=0

a = 10; b = -43; c = -17;
Δ = b2-4ac
Δ = -432-4·10·(-17)
Δ = 2529
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:

$\sqrt{\Delta}=\sqrt{2529}=\sqrt{9*281}=\sqrt{9}*\sqrt{281}=3\sqrt{281}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-3\sqrt{281}}{2*10}=\frac{43-3\sqrt{281}}{20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+3\sqrt{281}}{2*10}=\frac{43+3\sqrt{281}}{20}
$