x2-45x+342=0

Solution for x2-45x+342=0 equation:

x2-45x+342=0

We add all the numbers together, and all the variables

x^2-45x+342=0

a = 1; b = -45; c = +342;
Δ = b2-4ac
Δ = -452-4·1·342
Δ = 657
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{73}}{2*1}=\frac{45-3\sqrt{73}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{73}}{2*1}=\frac{45+3\sqrt{73}}{2}
$