# How do you solve 5x^2 - 2x + 16 = 4x^2 + 6x?

Sep 16, 2016

$x = 4$

#### Explanation:

We have: $5 {x}^{2} - 2 x + 16 = 4 {x}^{2} + 6 x$

First, let's subtract $4 {x}^{2} + 6 x$ from both sides of the equation:

$\implies {x}^{2} - 8 x + 16 = 0$

Then, let's factorise the equation using the middle-term break:

$\implies {x}^{2} - 4 x - 4 x + 16 = 0$

$\implies x \left(x - 4\right) - 4 \left(x - 4\right) = 0$

$\implies \left(x - 4\right) \left(x - 4\right) = 0$

$\implies {\left(x - 4\right)}^{2} = 0$

$\implies x - 4 = 0$

$\implies x = 4$

Therefore, the solution to the equation is $x = 4$.