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-9x(x+5)=6=-12
We move all terms to the left:
-9x(x+5)-(6)=0
We multiply parentheses
-9x^2-45x-6=0
a = -9; b = -45; c = -6;
Δ = b2-4ac
Δ = -452-4·(-9)·(-6)
Δ = 1809
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1809}=\sqrt{9*201}=\sqrt{9}*\sqrt{201}=3\sqrt{201}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{201}}{2*-9}=\frac{45-3\sqrt{201}}{-18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{201}}{2*-9}=\frac{45+3\sqrt{201}}{-18} $
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