w2+14w+43=0

Solution for w2+14w+43=0 equation:

w2+14w+43=0

We add all the numbers together, and all the variables

w^2+14w+43=0

a = 1; b = 14; c = +43;
Δ = b2-4ac
Δ = 142-4·1·43
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{6}}{2*1}=\frac{-14-2\sqrt{6}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{6}}{2*1}=\frac{-14+2\sqrt{6}}{2}
$