-5x^2+14x+29=0

Solution for -5x^2+14x+29=0 equation:

-5x^2+14x+29=0

a = -5; b = 14; c = +29;
Δ = b2-4ac
Δ = 142-4·(-5)·29
Δ = 776
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:

$\sqrt{\Delta}=\sqrt{776}=\sqrt{4*194}=\sqrt{4}*\sqrt{194}=2\sqrt{194}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{194}}{2*-5}=\frac{-14-2\sqrt{194}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{194}}{2*-5}=\frac{-14+2\sqrt{194}}{-10}
$