5x2=2-9x

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Solution for 5x2=2-9x equation:



5x^2=2-9x
We move all terms to the left:
5x^2-(2-9x)=0
We add all the numbers together, and all the variables
5x^2-(-9x+2)=0
We get rid of parentheses
5x^2+9x-2=0
a = 5; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·5·(-2)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-11}{2*5}=\frac{-20}{10} =-2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+11}{2*5}=\frac{2}{10} =1/5 $

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