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6x^2-14x=3x+7
We move all terms to the left:
6x^2-14x-(3x+7)=0
We get rid of parentheses
6x^2-14x-3x-7=0
We add all the numbers together, and all the variables
6x^2-17x-7=0
a = 6; b = -17; c = -7;
Δ = b2-4ac
Δ = -172-4·6·(-7)
Δ = 457
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{457}}{2*6}=\frac{17-\sqrt{457}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{457}}{2*6}=\frac{17+\sqrt{457}}{12} $
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