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6x^2=15x-6
We move all terms to the left:
6x^2-(15x-6)=0
We get rid of parentheses
6x^2-15x+6=0
a = 6; b = -15; c = +6;
Δ = b2-4ac
Δ = -152-4·6·6
Δ = 81
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{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-9}{2*6}=\frac{6}{12} =1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+9}{2*6}=\frac{24}{12} =2 $
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