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9x^2+2=27-3x
We move all terms to the left:
9x^2+2-(27-3x)=0
We add all the numbers together, and all the variables
9x^2-(-3x+27)+2=0
We get rid of parentheses
9x^2+3x-27+2=0
We add all the numbers together, and all the variables
9x^2+3x-25=0
a = 9; b = 3; c = -25;
Δ = b2-4ac
Δ = 32-4·9·(-25)
Δ = 909
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{909}=\sqrt{9*101}=\sqrt{9}*\sqrt{101}=3\sqrt{101}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{101}}{2*9}=\frac{-3-3\sqrt{101}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{101}}{2*9}=\frac{-3+3\sqrt{101}}{18} $
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