Question

Solve for $x$x:

$2x^{2}4x6=0$2x24x6=0

Solution

We use the Quadratic Formula:

-10-8-6-4-2246810-20-1010203040-2.002.00

$x=\frac{b\sqrt{b^{2}4ac}}{2a}$x=2abb24ac

For the equation:

• $a=2$a=2
• $b=4$b=4
• $c=6$c=6

Step 1: Substitute values

$x=\frac{(4)\sqrt{(4{)}^{2}4(2\left)\right(6)}}{2\left(2\right)}$x=2(2)(4)(4)24(2)(6)

Step 2: Simplify

$x=\frac{4\sqrt{16+48}}{4}$x=4416+48

$x=\frac{4\sqrt{64}}{4}$x=4464

Step 3: Final calculation

$x=\frac{48}{4}$x=448

So:

• $x=\frac{4+8}{4}=3$x=44+8=3
• $x=\frac{48}{4}=1$x=448=1

Final Answer

$x=3\text{or}x=1$x=3orx=1$$

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