7+x^2-14x=20+7

Solution for 7+x^2-14x=20+7 equation:

7+x^2-14x=20+7

We move all terms to the left:

7+x^2-14x-(20+7)=0

We add all the numbers together, and all the variables

x^2-14x+7-27=0

We add all the numbers together, and all the variables

x^2-14x-20=0

a = 1; b = -14; c = -20;
Δ = b2-4ac
Δ = -142-4·1·(-20)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{69}}{2*1}=\frac{14-2\sqrt{69}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{69}}{2*1}=\frac{14+2\sqrt{69}}{2}
$