(x^2-3)=(2x+14)

Solution for (x^2-3)=(2x+14) equation:

(x^2-3)=(2x+14)

We move all terms to the left:

(x^2-3)-((2x+14))=0

We get rid of parentheses

x^2-((2x+14))-3=0


We calculate terms in parentheses: -((2x+14)), so:

(2x+14)

We get rid of parentheses

2x+14

Back to the equation:

-(2x+14)


We get rid of parentheses

x^2-2x-14-3=0

We add all the numbers together, and all the variables

x^2-2x-17=0

a = 1; b = -2; c = -17;
Δ = b2-4ac
Δ = -22-4·1·(-17)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{2}}{2*1}=\frac{2-6\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{2}}{2*1}=\frac{2+6\sqrt{2}}{2}
$