41x=4x^2-784

Solution for 41x=4x^2-784 equation:

41x=4x^2-784

We move all terms to the left:

41x-(4x^2-784)=0

We get rid of parentheses

-4x^2+41x+784=0

a = -4; b = 41; c = +784;
Δ = b2-4ac
Δ = 412-4·(-4)·784
Δ = 14225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14225}=\sqrt{25*569}=\sqrt{25}*\sqrt{569}=5\sqrt{569}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-5\sqrt{569}}{2*-4}=\frac{-41-5\sqrt{569}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+5\sqrt{569}}{2*-4}=\frac{-41+5\sqrt{569}}{-8}
$