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6x^2-23x=18
We move all terms to the left:
6x^2-23x-(18)=0
a = 6; b = -23; c = -18;
Δ = b2-4ac
Δ = -232-4·6·(-18)
Δ = 961
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{961}=31$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-31}{2*6}=\frac{-8}{12} =-2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+31}{2*6}=\frac{54}{12} =4+1/2 $
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