X2+3x-109=0

Solution for X2+3x-109=0 equation:

X2+3X-109=0

We add all the numbers together, and all the variables

X^2+3X-109=0

a = 1; b = 3; c = -109;
Δ = b2-4ac
Δ = 32-4·1·(-109)
Δ = 445
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{-(3)-\sqrt{445}}{2*1}=\frac{-3-\sqrt{445}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{445}}{2*1}=\frac{-3+\sqrt{445}}{2}
$