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5x-6=7x-9x^2
We move all terms to the left:
5x-6-(7x-9x^2)=0
We get rid of parentheses
9x^2-7x+5x-6=0
We add all the numbers together, and all the variables
9x^2-2x-6=0
a = 9; b = -2; c = -6;
Δ = b2-4ac
Δ = -22-4·9·(-6)
Δ = 220
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{55}}{2*9}=\frac{2-2\sqrt{55}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{55}}{2*9}=\frac{2+2\sqrt{55}}{18} $
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