X2+4x=46

Solution for X2+4x=46 equation:

X2+4X=46

We move all terms to the left:

X2+4X-(46)=0

We add all the numbers together, and all the variables

X^2+4X-46=0

a = 1; b = 4; c = -46;
Δ = b2-4ac
Δ = 42-4·1·(-46)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-10\sqrt{2}}{2*1}=\frac{-4-10\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+10\sqrt{2}}{2*1}=\frac{-4+10\sqrt{2}}{2}
$