10x^2-25=x

Solution for 10x^2-25=x equation:

10x^2-25=x

We move all terms to the left:

10x^2-25-(x)=0

We add all the numbers together, and all the variables

10x^2-1x-25=0

a = 10; b = -1; c = -25;
Δ = b2-4ac
Δ = -12-4·10·(-25)
Δ = 1001
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{1001}}{2*10}=\frac{1-\sqrt{1001}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1001}}{2*10}=\frac{1+\sqrt{1001}}{20}
$