29x^2-101x-40=0

Solution for 29x^2-101x-40=0 equation:

29x^2-101x-40=0

a = 29; b = -101; c = -40;
Δ = b2-4ac
Δ = -1012-4·29·(-40)
Δ = 14841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14841}=\sqrt{9*1649}=\sqrt{9}*\sqrt{1649}=3\sqrt{1649}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-101)-3\sqrt{1649}}{2*29}=\frac{101-3\sqrt{1649}}{58}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-101)+3\sqrt{1649}}{2*29}=\frac{101+3\sqrt{1649}}{58}
$