Evaluate
87-14x-6x^{2}
Factor
-6\left(x-\frac{-\sqrt{571}-7}{6}\right)\left(x-\frac{\sqrt{571}-7}{6}\right)
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-6x^{2}+74x+7-88x+80
Combine 33x^{2} and -39x^{2} to get -6x^{2}.
-6x^{2}-14x+7+80
Combine 74x and -88x to get -14x.
-6x^{2}-14x+87
Add 7 and 80 to get 87.
factor(-6x^{2}+74x+7-88x+80)
Combine 33x^{2} and -39x^{2} to get -6x^{2}.
factor(-6x^{2}-14x+7+80)
Combine 74x and -88x to get -14x.
factor(-6x^{2}-14x+87)
Add 7 and 80 to get 87.
-6x^{2}-14x+87=0
Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.
x=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\left(-6\right)\times 87}}{2\left(-6\right)}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x=\frac{-\left(-14\right)±\sqrt{196-4\left(-6\right)\times 87}}{2\left(-6\right)}
Square -14.
x=\frac{-\left(-14\right)±\sqrt{196+24\times 87}}{2\left(-6\right)}
Multiply -4 times -6.
x=\frac{-\left(-14\right)±\sqrt{196+2088}}{2\left(-6\right)}
Multiply 24 times 87.
x=\frac{-\left(-14\right)±\sqrt{2284}}{2\left(-6\right)}
Add 196 to 2088.
x=\frac{-\left(-14\right)±2\sqrt{571}}{2\left(-6\right)}
Take the square root of 2284.
x=\frac{14±2\sqrt{571}}{2\left(-6\right)}
The opposite of -14 is 14.
x=\frac{14±2\sqrt{571}}{-12}
Multiply 2 times -6.
x=\frac{2\sqrt{571}+14}{-12}
Now solve the equation x=\frac{14±2\sqrt{571}}{-12} when ± is plus. Add 14 to 2\sqrt{571}.
x=\frac{-\sqrt{571}-7}{6}
Divide 14+2\sqrt{571} by -12.
x=\frac{14-2\sqrt{571}}{-12}
Now solve the equation x=\frac{14±2\sqrt{571}}{-12} when ± is minus. Subtract 2\sqrt{571} from 14.
x=\frac{\sqrt{571}-7}{6}
Divide 14-2\sqrt{571} by -12.
-6x^{2}-14x+87=-6\left(x-\frac{-\sqrt{571}-7}{6}\right)\left(x-\frac{\sqrt{571}-7}{6}\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-7-\sqrt{571}}{6} for x_{1} and \frac{-7+\sqrt{571}}{6} for x_{2}.
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