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0=-9x^2-5x+3
We move all terms to the left:
0-(-9x^2-5x+3)=0
We add all the numbers together, and all the variables
-(-9x^2-5x+3)=0
We get rid of parentheses
9x^2+5x-3=0
a = 9; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·9·(-3)
Δ = 133
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{-(5)-\sqrt{133}}{2*9}=\frac{-5-\sqrt{133}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{133}}{2*9}=\frac{-5+\sqrt{133}}{18} $
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