8x2-1=24-x

Solution for 8x2-1=24-x equation:

8x^2-1=24-x

We move all terms to the left:

8x^2-1-(24-x)=0

We add all the numbers together, and all the variables

8x^2-(-1x+24)-1=0

We get rid of parentheses

8x^2+1x-24-1=0

We add all the numbers together, and all the variables

8x^2+x-25=0

a = 8; b = 1; c = -25;
Δ = b2-4ac
Δ = 12-4·8·(-25)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{89}}{2*8}=\frac{-1-3\sqrt{89}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{89}}{2*8}=\frac{-1+3\sqrt{89}}{16}
$