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9X^2=-4X+9
We move all terms to the left:
9X^2-(-4X+9)=0
We get rid of parentheses
9X^2+4X-9=0
a = 9; b = 4; c = -9;
Δ = b2-4ac
Δ = 42-4·9·(-9)
Δ = 340
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{85}}{2*9}=\frac{-4-2\sqrt{85}}{18} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{85}}{2*9}=\frac{-4+2\sqrt{85}}{18} $
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