X2-47x+462=0

Solution for X2-47x+462=0 equation:

X2-47X+462=0

We add all the numbers together, and all the variables

X^2-47X+462=0

a = 1; b = -47; c = +462;
Δ = b2-4ac
Δ = -472-4·1·462
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-19}{2*1}=\frac{28}{2}
=14
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+19}{2*1}=\frac{66}{2}
=33
$