Answer:
[tex]x=\frac{-5+\sqrt{33}}{2},\:x=\frac{-5-\sqrt{33}}{2}[/tex]
Step-by-step explanation:
The given equation is [tex]2x(x+5)=4[/tex]
Distribute 2x over the parentheses
[tex]2x^2+10x=4[/tex]
Subtract 4 to both sides of the equation
[tex]2x^2+10x-4=0[/tex]
We can take 2 common and rewrite the equation as
[tex]x^2+5x-2=0[/tex]
Apply the quadratic formula, [tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex], we get
[tex]x_{1,\:2}=\frac{-5\pm \sqrt{5^2-4\cdot \:1\left(-2\right)}}{2\cdot \:1}[/tex]
Simplifying we get
[tex]\frac{-5\pm\sqrt{33}}{2\cdot \:1}[/tex]
Thus, the solution to the given quadratic equation is
[tex]x=\frac{-5+\sqrt{33}}{2},\:x=\frac{-5-\sqrt{33}}{2}[/tex]
