2x^2-46x+4=890

Solution for 2x^2-46x+4=890 equation:

2x^2-46x+4=890

We move all terms to the left:

2x^2-46x+4-(890)=0

We add all the numbers together, and all the variables

2x^2-46x-886=0

a = 2; b = -46; c = -886;
Δ = b2-4ac
Δ = -462-4·2·(-886)
Δ = 9204
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:

$\sqrt{\Delta}=\sqrt{9204}=\sqrt{4*2301}=\sqrt{4}*\sqrt{2301}=2\sqrt{2301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{2301}}{2*2}=\frac{46-2\sqrt{2301}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{2301}}{2*2}=\frac{46+2\sqrt{2301}}{4}
$