6x^2+82x-5500=0

Solution for 6x^2+82x-5500=0 equation:

6x^2+82x-5500=0

a = 6; b = 82; c = -5500;
Δ = b2-4ac
Δ = 822-4·6·(-5500)
Δ = 138724
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:

$\sqrt{\Delta}=\sqrt{138724}=\sqrt{4*34681}=\sqrt{4}*\sqrt{34681}=2\sqrt{34681}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-2\sqrt{34681}}{2*6}=\frac{-82-2\sqrt{34681}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+2\sqrt{34681}}{2*6}=\frac{-82+2\sqrt{34681}}{12}
$