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6x^{2}+3x=2+4x
Use the distributive property to multiply 3x by 2x+1.
6x^{2}+3x-2=4x
Subtract 2 from both sides.
6x^{2}+3x-2-4x=0
Subtract 4x from both sides.
6x^{2}-x-2=0
Combine 3x and -4x to get -x.
x=\frac{-\left(-1\right)±\sqrt{1-4\times 6\left(-2\right)}}{2\times 6}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, -1 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-1\right)±\sqrt{1-24\left(-2\right)}}{2\times 6}
Multiply -4 times 6.
x=\frac{-\left(-1\right)±\sqrt{1+48}}{2\times 6}
Multiply -24 times -2.
x=\frac{-\left(-1\right)±\sqrt{49}}{2\times 6}
Add 1 to 48.
x=\frac{-\left(-1\right)±7}{2\times 6}
Take the square root of 49.
x=\frac{1±7}{2\times 6}
The opposite of -1 is 1.
x=\frac{1±7}{12}
Multiply 2 times 6.
x=\frac{8}{12}
Now solve the equation x=\frac{1±7}{12} when ± is plus. Add 1 to 7.
x=\frac{2}{3}
Reduce the fraction \frac{8}{12} to lowest terms by extracting and canceling out 4.
x=-\frac{6}{12}
Now solve the equation x=\frac{1±7}{12} when ± is minus. Subtract 7 from 1.
x=-\frac{1}{2}
Reduce the fraction \frac{-6}{12} to lowest terms by extracting and canceling out 6.
x=\frac{2}{3} x=-\frac{1}{2}
The equation is now solved.
6x^{2}+3x=2+4x
Use the distributive property to multiply 3x by 2x+1.
6x^{2}+3x-4x=2
Subtract 4x from both sides.
6x^{2}-x=2
Combine 3x and -4x to get -x.
\frac{6x^{2}-x}{6}=\frac{2}{6}
Divide both sides by 6.
x^{2}-\frac{1}{6}x=\frac{2}{6}
Dividing by 6 undoes the multiplication by 6.
x^{2}-\frac{1}{6}x=\frac{1}{3}
Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.
x^{2}-\frac{1}{6}x+\left(-\frac{1}{12}\right)^{2}=\frac{1}{3}+\left(-\frac{1}{12}\right)^{2}
Divide -\frac{1}{6}, the coefficient of the x term, by 2 to get -\frac{1}{12}. Then add the square of -\frac{1}{12} to both sides of the equation. This step makes the left hand side of the equation a perfect square.
x^{2}-\frac{1}{6}x+\frac{1}{144}=\frac{1}{3}+\frac{1}{144}
Square -\frac{1}{12} by squaring both the numerator and the denominator of the fraction.
x^{2}-\frac{1}{6}x+\frac{1}{144}=\frac{49}{144}
Add \frac{1}{3} to \frac{1}{144} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
\left(x-\frac{1}{12}\right)^{2}=\frac{49}{144}
Factor x^{2}-\frac{1}{6}x+\frac{1}{144}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.
\sqrt{\left(x-\frac{1}{12}\right)^{2}}=\sqrt{\frac{49}{144}}
Take the square root of both sides of the equation.
x-\frac{1}{12}=\frac{7}{12} x-\frac{1}{12}=-\frac{7}{12}
Simplify.
x=\frac{2}{3} x=-\frac{1}{2}
Add \frac{1}{12} to both sides of the equation.