5x^2-34x-84=0

Solution for 5x^2-34x-84=0 equation:

5x^2-34x-84=0

a = 5; b = -34; c = -84;
Δ = b2-4ac
Δ = -342-4·5·(-84)
Δ = 2836
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:

$\sqrt{\Delta}=\sqrt{2836}=\sqrt{4*709}=\sqrt{4}*\sqrt{709}=2\sqrt{709}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{709}}{2*5}=\frac{34-2\sqrt{709}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{709}}{2*5}=\frac{34+2\sqrt{709}}{10}
$