x^2+4x-7=12

Solution for x^2+4x-7=12 equation:

x^2+4x-7=12

We move all terms to the left:

x^2+4x-7-(12)=0

We add all the numbers together, and all the variables

x^2+4x-19=0

a = 1; b = 4; c = -19;
Δ = b2-4ac
Δ = 42-4·1·(-19)
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{23}}{2*1}=\frac{-4-2\sqrt{23}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{23}}{2*1}=\frac{-4+2\sqrt{23}}{2}
$