15x^2-62x-29=0

Solution for 15x^2-62x-29=0 equation:

15x^2-62x-29=0

a = 15; b = -62; c = -29;
Δ = b2-4ac
Δ = -622-4·15·(-29)
Δ = 5584
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:

$\sqrt{\Delta}=\sqrt{5584}=\sqrt{16*349}=\sqrt{16}*\sqrt{349}=4\sqrt{349}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-4\sqrt{349}}{2*15}=\frac{62-4\sqrt{349}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+4\sqrt{349}}{2*15}=\frac{62+4\sqrt{349}}{30}
$