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3x(3x+4)-5=-2
We move all terms to the left:
3x(3x+4)-5-(-2)=0
We add all the numbers together, and all the variables
3x(3x+4)-3=0
We multiply parentheses
9x^2+12x-3=0
a = 9; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·9·(-3)
Δ = 252
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{7}}{2*9}=\frac{-12-6\sqrt{7}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{7}}{2*9}=\frac{-12+6\sqrt{7}}{18} $
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