x^2-30x=29=0

Solution for x^2-30x=29=0 equation:

x^2-30x=29=0

We move all terms to the left:

x^2-30x-(29)=0

a = 1; b = -30; c = -29;
Δ = b2-4ac
Δ = -302-4·1·(-29)
Δ = 1016
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:

$\sqrt{\Delta}=\sqrt{1016}=\sqrt{4*254}=\sqrt{4}*\sqrt{254}=2\sqrt{254}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{254}}{2*1}=\frac{30-2\sqrt{254}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{254}}{2*1}=\frac{30+2\sqrt{254}}{2}
$