X^2-7x-343=3x

Solution for X^2-7x-343=3x equation:

X^2-7X-343=3X

We move all terms to the left:

X^2-7X-343-(3X)=0

We add all the numbers together, and all the variables

X^2-10X-343=0

a = 1; b = -10; c = -343;
Δ = b2-4ac
Δ = -102-4·1·(-343)
Δ = 1472
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:

$\sqrt{\Delta}=\sqrt{1472}=\sqrt{64*23}=\sqrt{64}*\sqrt{23}=8\sqrt{23}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-8\sqrt{23}}{2*1}=\frac{10-8\sqrt{23}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+8\sqrt{23}}{2*1}=\frac{10+8\sqrt{23}}{2}
$