X^2+6x-46=0

Solution for X^2+6x-46=0 equation:

X^2+6X-46=0

a = 1; b = 6; c = -46;
Δ = b2-4ac
Δ = 62-4·1·(-46)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{55}}{2*1}=\frac{-6-2\sqrt{55}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{55}}{2*1}=\frac{-6+2\sqrt{55}}{2}
$