x^2+46x=420

Solution for x^2+46x=420 equation:

x^2+46x=420

We move all terms to the left:

x^2+46x-(420)=0

a = 1; b = 46; c = -420;
Δ = b2-4ac
Δ = 462-4·1·(-420)
Δ = 3796
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:

$\sqrt{\Delta}=\sqrt{3796}=\sqrt{4*949}=\sqrt{4}*\sqrt{949}=2\sqrt{949}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{949}}{2*1}=\frac{-46-2\sqrt{949}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{949}}{2*1}=\frac{-46+2\sqrt{949}}{2}
$