X^2+6x=105

Solution for X^2+6x=105 equation:

X^2+6X=105

We move all terms to the left:

X^2+6X-(105)=0

a = 1; b = 6; c = -105;
Δ = b2-4ac
Δ = 62-4·1·(-105)
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{114}}{2*1}=\frac{-6-2\sqrt{114}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{114}}{2*1}=\frac{-6+2\sqrt{114}}{2}
$