w^2-22w=43

Solution for w^2-22w=43 equation:

w^2-22w=43

We move all terms to the left:

w^2-22w-(43)=0

a = 1; b = -22; c = -43;
Δ = b2-4ac
Δ = -222-4·1·(-43)
Δ = 656
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:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-4\sqrt{41}}{2*1}=\frac{22-4\sqrt{41}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+4\sqrt{41}}{2*1}=\frac{22+4\sqrt{41}}{2}
$