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6x(x-3)=3x+7
We move all terms to the left:
6x(x-3)-(3x+7)=0
We multiply parentheses
6x^2-18x-(3x+7)=0
We get rid of parentheses
6x^2-18x-3x-7=0
We add all the numbers together, and all the variables
6x^2-21x-7=0
a = 6; b = -21; c = -7;
Δ = b2-4ac
Δ = -212-4·6·(-7)
Δ = 609
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{-(-21)-\sqrt{609}}{2*6}=\frac{21-\sqrt{609}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{609}}{2*6}=\frac{21+\sqrt{609}}{12} $
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