5x2-10x=20

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Solution for 5x2-10x=20 equation:



5x^2-10x=20
We move all terms to the left:
5x^2-10x-(20)=0
a = 5; b = -10; c = -20;
Δ = b2-4ac
Δ = -102-4·5·(-20)
Δ = 500
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:
$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{5}}{2*5}=\frac{10-10\sqrt{5}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{5}}{2*5}=\frac{10+10\sqrt{5}}{10} $

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