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3x(-11+3x)=x+19
We move all terms to the left:
3x(-11+3x)-(x+19)=0
We add all the numbers together, and all the variables
3x(3x-11)-(x+19)=0
We multiply parentheses
9x^2-33x-(x+19)=0
We get rid of parentheses
9x^2-33x-x-19=0
We add all the numbers together, and all the variables
9x^2-34x-19=0
a = 9; b = -34; c = -19;
Δ = b2-4ac
Δ = -342-4·9·(-19)
Δ = 1840
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-4\sqrt{115}}{2*9}=\frac{34-4\sqrt{115}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+4\sqrt{115}}{2*9}=\frac{34+4\sqrt{115}}{18} $
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