2x^2-10x+25=18,75

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Solution for 2x^2-10x+25=18,75 equation:



2x^2-10x+25=18.75
We move all terms to the left:
2x^2-10x+25-(18.75)=0
We add all the numbers together, and all the variables
2x^2-10x+6.25=0
a = 2; b = -10; c = +6.25;
Δ = b2-4ac
Δ = -102-4·2·6.25
Δ = 50
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:
$\sqrt{\Delta}=\sqrt{50}=\sqrt{25*2}=\sqrt{25}*\sqrt{2}=5\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-5\sqrt{2}}{2*2}=\frac{10-5\sqrt{2}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+5\sqrt{2}}{2*2}=\frac{10+5\sqrt{2}}{4} $

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