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7x-9x^2=x-6
We move all terms to the left:
7x-9x^2-(x-6)=0
We get rid of parentheses
-9x^2+7x-x+6=0
We add all the numbers together, and all the variables
-9x^2+6x+6=0
a = -9; b = 6; c = +6;
Δ = b2-4ac
Δ = 62-4·(-9)·6
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{-(6)-6\sqrt{7}}{2*-9}=\frac{-6-6\sqrt{7}}{-18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{7}}{2*-9}=\frac{-6+6\sqrt{7}}{-18} $
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