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10-6x-9x^2=9x
We move all terms to the left:
10-6x-9x^2-(9x)=0
We add all the numbers together, and all the variables
-9x^2-15x+10=0
a = -9; b = -15; c = +10;
Δ = b2-4ac
Δ = -152-4·(-9)·10
Δ = 585
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{65}}{2*-9}=\frac{15-3\sqrt{65}}{-18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{65}}{2*-9}=\frac{15+3\sqrt{65}}{-18} $
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