X^2-130x-6000=0

Solution for X^2-130x-6000=0 equation:

X^2-130X-6000=0

a = 1; b = -130; c = -6000;
Δ = b2-4ac
Δ = -1302-4·1·(-6000)
Δ = 40900
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:

$\sqrt{\Delta}=\sqrt{40900}=\sqrt{100*409}=\sqrt{100}*\sqrt{409}=10\sqrt{409}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-10\sqrt{409}}{2*1}=\frac{130-10\sqrt{409}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+10\sqrt{409}}{2*1}=\frac{130+10\sqrt{409}}{2}
$