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7x-9x^2=6x-6
We move all terms to the left:
7x-9x^2-(6x-6)=0
We get rid of parentheses
-9x^2+7x-6x+6=0
We add all the numbers together, and all the variables
-9x^2+x+6=0
a = -9; b = 1; c = +6;
Δ = b2-4ac
Δ = 12-4·(-9)·6
Δ = 217
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{217}}{2*-9}=\frac{-1-\sqrt{217}}{-18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{217}}{2*-9}=\frac{-1+\sqrt{217}}{-18} $
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