X2-7x-109=0

Solution for X2-7x-109=0 equation:

X2-7X-109=0

We add all the numbers together, and all the variables

X^2-7X-109=0

a = 1; b = -7; c = -109;
Δ = b2-4ac
Δ = -72-4·1·(-109)
Δ = 485
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{485}}{2*1}=\frac{7-\sqrt{485}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{485}}{2*1}=\frac{7+\sqrt{485}}{2}
$