(x)=-5x^2+3x+1

Solution for (x)=-5x^2+3x+1 equation:

(x)=-5x^2+3x+1

We move all terms to the left:

(x)-(-5x^2+3x+1)=0

We get rid of parentheses

5x^2-3x+x-1=0

We add all the numbers together, and all the variables

5x^2-2x-1=0

a = 5; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·5·(-1)
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{6}}{2*5}=\frac{2-2\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{6}}{2*5}=\frac{2+2\sqrt{6}}{10}
$