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3x^2-17x=10
We move all terms to the left:
3x^2-17x-(10)=0
a = 3; b = -17; c = -10;
Δ = b2-4ac
Δ = -172-4·3·(-10)
Δ = 409
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{-(-17)-\sqrt{409}}{2*3}=\frac{17-\sqrt{409}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{409}}{2*3}=\frac{17+\sqrt{409}}{6} $
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