y2-42y+43=0

Solution for y2-42y+43=0 equation:

y2-42y+43=0

We add all the numbers together, and all the variables

y^2-42y+43=0

a = 1; b = -42; c = +43;
Δ = b2-4ac
Δ = -422-4·1·43
Δ = 1592
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1592}=\sqrt{4*398}=\sqrt{4}*\sqrt{398}=2\sqrt{398}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{398}}{2*1}=\frac{42-2\sqrt{398}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{398}}{2*1}=\frac{42+2\sqrt{398}}{2}
$