29a^2-7a-40=0

Solution for 29a^2-7a-40=0 equation:

29a^2-7a-40=0

a = 29; b = -7; c = -40;
Δ = b2-4ac
Δ = -72-4·29·(-40)
Δ = 4689
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:

$\sqrt{\Delta}=\sqrt{4689}=\sqrt{9*521}=\sqrt{9}*\sqrt{521}=3\sqrt{521}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3\sqrt{521}}{2*29}=\frac{7-3\sqrt{521}}{58}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3\sqrt{521}}{2*29}=\frac{7+3\sqrt{521}}{58}
$