x2+52;x=3

Solution for x2+52;x=3 equation:

x2+52x=3

We move all terms to the left:

x2+52x-(3)=0

We add all the numbers together, and all the variables

x^2+52x-3=0

a = 1; b = 52; c = -3;
Δ = b2-4ac
Δ = 522-4·1·(-3)
Δ = 2716
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:

$\sqrt{\Delta}=\sqrt{2716}=\sqrt{4*679}=\sqrt{4}*\sqrt{679}=2\sqrt{679}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-2\sqrt{679}}{2*1}=\frac{-52-2\sqrt{679}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+2\sqrt{679}}{2*1}=\frac{-52+2\sqrt{679}}{2}
$