8x^2-1-x=-x+5

Solution for 8x^2-1-x=-x+5 equation:

8x^2-1-x=-x+5

We move all terms to the left:

8x^2-1-x-(-x+5)=0

We add all the numbers together, and all the variables

8x^2-x-(-1x+5)-1=0

We add all the numbers together, and all the variables

8x^2-1x-(-1x+5)-1=0

We get rid of parentheses

8x^2-1x+1x-5-1=0

We add all the numbers together, and all the variables

8x^2-6=0

a = 8; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·8·(-6)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*8}=\frac{0-8\sqrt{3}}{16}
=-\frac{8\sqrt{3}}{16}
=-\frac{\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*8}=\frac{0+8\sqrt{3}}{16}
=\frac{8\sqrt{3}}{16}
=\frac{\sqrt{3}}{2}
$