52x^2+x=10

Solution for 52x^2+x=10 equation:

52x^2+x=10

We move all terms to the left:

52x^2+x-(10)=0

a = 52; b = 1; c = -10;
Δ = b2-4ac
Δ = 12-4·52·(-10)
Δ = 2081
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{2081}}{2*52}=\frac{-1-\sqrt{2081}}{104}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{2081}}{2*52}=\frac{-1+\sqrt{2081}}{104}
$