50+50-25x2+2+2=54

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Solution for 50+50-25x2+2+2=54 equation:



50+50-25x^2+2+2=54
We move all terms to the left:
50+50-25x^2+2+2-(54)=0
We add all the numbers together, and all the variables
-25x^2+50=0
a = -25; b = 0; c = +50;
Δ = b2-4ac
Δ = 02-4·(-25)·50
Δ = 5000
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:
$\sqrt{\Delta}=\sqrt{5000}=\sqrt{2500*2}=\sqrt{2500}*\sqrt{2}=50\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-50\sqrt{2}}{2*-25}=\frac{0-50\sqrt{2}}{-50} =-\frac{50\sqrt{2}}{-50} =-\frac{\sqrt{2}}{-1} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+50\sqrt{2}}{2*-25}=\frac{0+50\sqrt{2}}{-50} =\frac{50\sqrt{2}}{-50} =\frac{\sqrt{2}}{-1} $

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