x^2-53*x+376=0

Solution for x^2-53*x+376=0 equation:

x^2-53x+376=0

a = 1; b = -53; c = +376;
Δ = b2-4ac
Δ = -532-4·1·376
Δ = 1305
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:

$\sqrt{\Delta}=\sqrt{1305}=\sqrt{9*145}=\sqrt{9}*\sqrt{145}=3\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-3\sqrt{145}}{2*1}=\frac{53-3\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+3\sqrt{145}}{2*1}=\frac{53+3\sqrt{145}}{2}
$