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2000-310x+9x^2=0
a = 9; b = -310; c = +2000;
Δ = b2-4ac
Δ = -3102-4·9·2000
Δ = 24100
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{24100}=\sqrt{100*241}=\sqrt{100}*\sqrt{241}=10\sqrt{241}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-310)-10\sqrt{241}}{2*9}=\frac{310-10\sqrt{241}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-310)+10\sqrt{241}}{2*9}=\frac{310+10\sqrt{241}}{18} $
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