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6x(9x+3)=11-3x
We move all terms to the left:
6x(9x+3)-(11-3x)=0
We add all the numbers together, and all the variables
6x(9x+3)-(-3x+11)=0
We multiply parentheses
54x^2+18x-(-3x+11)=0
We get rid of parentheses
54x^2+18x+3x-11=0
We add all the numbers together, and all the variables
54x^2+21x-11=0
a = 54; b = 21; c = -11;
Δ = b2-4ac
Δ = 212-4·54·(-11)
Δ = 2817
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2817}=\sqrt{9*313}=\sqrt{9}*\sqrt{313}=3\sqrt{313}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{313}}{2*54}=\frac{-21-3\sqrt{313}}{108} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{313}}{2*54}=\frac{-21+3\sqrt{313}}{108} $
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