x^2+30x=840

Solution for x^2+30x=840 equation:

x^2+30x=840

We move all terms to the left:

x^2+30x-(840)=0

a = 1; b = 30; c = -840;
Δ = b2-4ac
Δ = 302-4·1·(-840)
Δ = 4260
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:

$\sqrt{\Delta}=\sqrt{4260}=\sqrt{4*1065}=\sqrt{4}*\sqrt{1065}=2\sqrt{1065}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{1065}}{2*1}=\frac{-30-2\sqrt{1065}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{1065}}{2*1}=\frac{-30+2\sqrt{1065}}{2}
$