x2-42x+185=0

Solution for x2-42x+185=0 equation:

x2-42x+185=0

We add all the numbers together, and all the variables

x^2-42x+185=0

a = 1; b = -42; c = +185;
Δ = b2-4ac
Δ = -422-4·1·185
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-32}{2*1}=\frac{10}{2}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+32}{2*1}=\frac{74}{2}
=37
$