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-5x^{2}+8x+2=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{-8±\sqrt{8^{2}-4\left(-5\right)\times 2}}{2\left(-5\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{-8±\sqrt{64-4\left(-5\right)\times 2}}{2\left(-5\right)}
Square 8.
x=\frac{-8±\sqrt{64+20\times 2}}{2\left(-5\right)}
Multiply -4 times -5.
x=\frac{-8±\sqrt{64+40}}{2\left(-5\right)}
Multiply 20 times 2.
x=\frac{-8±\sqrt{104}}{2\left(-5\right)}
Add 64 to 40.
x=\frac{-8±2\sqrt{26}}{2\left(-5\right)}
Take the square root of 104.
x=\frac{-8±2\sqrt{26}}{-10}
Multiply 2 times -5.
x=\frac{2\sqrt{26}-8}{-10}
Now solve the equation x=\frac{-8±2\sqrt{26}}{-10} when ± is plus. Add -8 to 2\sqrt{26}.
x=\frac{4-\sqrt{26}}{5}
Divide -8+2\sqrt{26} by -10.
x=\frac{-2\sqrt{26}-8}{-10}
Now solve the equation x=\frac{-8±2\sqrt{26}}{-10} when ± is minus. Subtract 2\sqrt{26} from -8.
x=\frac{\sqrt{26}+4}{5}
Divide -8-2\sqrt{26} by -10.
-5x^{2}+8x+2=-5\left(x-\frac{4-\sqrt{26}}{5}\right)\left(x-\frac{\sqrt{26}+4}{5}\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{4-\sqrt{26}}{5} for x_{1} and \frac{4+\sqrt{26}}{5} for x_{2}.