5x^2-46x+51=0

Solution for 5x^2-46x+51=0 equation:

5x^2-46x+51=0

a = 5; b = -46; c = +51;
Δ = b2-4ac
Δ = -462-4·5·51
Δ = 1096
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:

$\sqrt{\Delta}=\sqrt{1096}=\sqrt{4*274}=\sqrt{4}*\sqrt{274}=2\sqrt{274}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{274}}{2*5}=\frac{46-2\sqrt{274}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{274}}{2*5}=\frac{46+2\sqrt{274}}{10}
$