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3x(x-2)=7x+1
We move all terms to the left:
3x(x-2)-(7x+1)=0
We multiply parentheses
3x^2-6x-(7x+1)=0
We get rid of parentheses
3x^2-6x-7x-1=0
We add all the numbers together, and all the variables
3x^2-13x-1=0
a = 3; b = -13; c = -1;
Δ = b2-4ac
Δ = -132-4·3·(-1)
Δ = 181
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{-(-13)-\sqrt{181}}{2*3}=\frac{13-\sqrt{181}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{181}}{2*3}=\frac{13+\sqrt{181}}{6} $
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