6x^2-16=5x^2-16x

Solution for 6x^2-16=5x^2-16x equation:

6x^2-16=5x^2-16x

We move all terms to the left:

6x^2-16-(5x^2-16x)=0

We get rid of parentheses

6x^2-5x^2+16x-16=0

We add all the numbers together, and all the variables

x^2+16x-16=0

a = 1; b = 16; c = -16;
Δ = b2-4ac
Δ = 162-4·1·(-16)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{5}}{2*1}=\frac{-16-8\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{5}}{2*1}=\frac{-16+8\sqrt{5}}{2}
$