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9x-9x^2=5x-6
We move all terms to the left:
9x-9x^2-(5x-6)=0
We get rid of parentheses
-9x^2+9x-5x+6=0
We add all the numbers together, and all the variables
-9x^2+4x+6=0
a = -9; b = 4; c = +6;
Δ = b2-4ac
Δ = 42-4·(-9)·6
Δ = 232
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{58}}{2*-9}=\frac{-4-2\sqrt{58}}{-18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{58}}{2*-9}=\frac{-4+2\sqrt{58}}{-18} $
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