10x^2-11=53x

Solution for 10x^2-11=53x equation:

10x^2-11=53x

We move all terms to the left:

10x^2-11-(53x)=0

a = 10; b = -53; c = -11;
Δ = b2-4ac
Δ = -532-4·10·(-11)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-57}{2*10}=\frac{-4}{20}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+57}{2*10}=\frac{110}{20}
=5+1/2
$