24-16x+3x^2=23-8x+x^2

Solution for 24-16x+3x^2=23-8x+x^2 equation:

24-16x+3x^2=23-8x+x^2

We move all terms to the left:

24-16x+3x^2-(23-8x+x^2)=0

We get rid of parentheses

3x^2-x^2+8x-16x-23+24=0

We add all the numbers together, and all the variables

2x^2-8x+1=0

a = 2; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·2·1
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{14}}{2*2}=\frac{8-2\sqrt{14}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{14}}{2*2}=\frac{8+2\sqrt{14}}{4}
$