X^2+5x-194=0

Solution for X^2+5x-194=0 equation:

X^2+5X-194=0

a = 1; b = 5; c = -194;
Δ = b2-4ac
Δ = 52-4·1·(-194)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{89}}{2*1}=\frac{-5-3\sqrt{89}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{89}}{2*1}=\frac{-5+3\sqrt{89}}{2}
$