x^2-30x+14=-1

Solution for x^2-30x+14=-1 equation:

x^2-30x+14=-1

We move all terms to the left:

x^2-30x+14-(-1)=0

We add all the numbers together, and all the variables

x^2-30x+15=0

a = 1; b = -30; c = +15;
Δ = b2-4ac
Δ = -302-4·1·15
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{210}}{2*1}=\frac{30-2\sqrt{210}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{210}}{2*1}=\frac{30+2\sqrt{210}}{2}
$