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7x-9x^2=-6
We move all terms to the left:
7x-9x^2-(-6)=0
We add all the numbers together, and all the variables
-9x^2+7x+6=0
a = -9; b = 7; c = +6;
Δ = b2-4ac
Δ = 72-4·(-9)·6
Δ = 265
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{-(7)-\sqrt{265}}{2*-9}=\frac{-7-\sqrt{265}}{-18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{265}}{2*-9}=\frac{-7+\sqrt{265}}{-18} $
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