s2+20s-43=0

Solution for s2+20s-43=0 equation:

s2+20s-43=0

We add all the numbers together, and all the variables

s^2+20s-43=0

a = 1; b = 20; c = -43;
Δ = b2-4ac
Δ = 202-4·1·(-43)
Δ = 572
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{572}=\sqrt{4*143}=\sqrt{4}*\sqrt{143}=2\sqrt{143}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{143}}{2*1}=\frac{-20-2\sqrt{143}}{2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{143}}{2*1}=\frac{-20+2\sqrt{143}}{2}
$