5x2-53=x

Solution for 5x2-53=x equation:

5x^2-53=x

We move all terms to the left:

5x^2-53-(x)=0

We add all the numbers together, and all the variables

5x^2-1x-53=0

a = 5; b = -1; c = -53;
Δ = b2-4ac
Δ = -12-4·5·(-53)
Δ = 1061
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{1061}}{2*5}=\frac{1-\sqrt{1061}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1061}}{2*5}=\frac{1+\sqrt{1061}}{10}
$