8x^2-35=x

Solution for 8x^2-35=x equation:

8x^2-35=x

We move all terms to the left:

8x^2-35-(x)=0

We add all the numbers together, and all the variables

8x^2-1x-35=0

a = 8; b = -1; c = -35;
Δ = b2-4ac
Δ = -12-4·8·(-35)
Δ = 1121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{1121}}{2*8}=\frac{1-\sqrt{1121}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1121}}{2*8}=\frac{1+\sqrt{1121}}{16}
$