5x^2+28x-82=0

Solution for 5x^2+28x-82=0 equation:

5x^2+28x-82=0

a = 5; b = 28; c = -82;
Δ = b2-4ac
Δ = 282-4·5·(-82)
Δ = 2424
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:

$\sqrt{\Delta}=\sqrt{2424}=\sqrt{4*606}=\sqrt{4}*\sqrt{606}=2\sqrt{606}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{606}}{2*5}=\frac{-28-2\sqrt{606}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{606}}{2*5}=\frac{-28+2\sqrt{606}}{10}
$