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6x+5=9x^2
We move all terms to the left:
6x+5-(9x^2)=0
determiningTheFunctionDomain -9x^2+6x+5=0
a = -9; b = 6; c = +5;
Δ = b2-4ac
Δ = 62-4·(-9)·5
Δ = 216
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{6}}{2*-9}=\frac{-6-6\sqrt{6}}{-18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{6}}{2*-9}=\frac{-6+6\sqrt{6}}{-18} $
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