-2x2 = -(5x + 4)
Distribute -1 to the terms in parenthesees.
-2x2 = -5x - 4
Add 2x2 to both sides of the equation.
0 = 2x2 - 5x - 4
2x2 - 5x - 4 = 0
2x2 + -5x + -4 = 0
This is a quadratic equation. We can use the quadratic formula to solve for x .
The quadratic formula says that....
If ax2 + bx + c = 0 then \( x=\frac{-\mathbf{\color{blue}b}\pm\sqrt{\mathbf{\color{blue}b}^2-4\mathbf{\color{Magenta}a}\mathbf{\color{Green}c}}}{2\mathbf{\color{Magenta}a}}\)
So...
Since 2x2 + -5x + -4 = 0 then \( x=\frac{-(\mathbf{\color{blue}-5})\pm\sqrt{\mathbf{(\color{blue}-5})^2-4(\mathbf{\color{Magenta}2})(\mathbf{\color{Green}-4})}}{2(\mathbf{\color{Magenta}2})}\)
\(x=\frac{-(-5)\pm\sqrt{(-5)^2-4(2)(-4)}}{2(2)}\\~\\ x=\frac{5\pm\sqrt{25+32}}{4}\\~\\ x=\frac{5\pm\sqrt{57}}{4}\\~\\ x=\frac{5+\sqrt{57}}{4}\qquad\text{or}\qquad x=\frac{5-\sqrt{57}}{4}\)