X^2-4x-45=7

Solution for X^2-4x-45=7 equation:

X^2-4X-45=7

We move all terms to the left:

X^2-4X-45-(7)=0

We add all the numbers together, and all the variables

X^2-4X-52=0

a = 1; b = -4; c = -52;
Δ = b2-4ac
Δ = -42-4·1·(-52)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{14}}{2*1}=\frac{4-4\sqrt{14}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{14}}{2*1}=\frac{4+4\sqrt{14}}{2}
$