x^2-7x-47=5x-2

Solution for x^2-7x-47=5x-2 equation:

x^2-7x-47=5x-2

We move all terms to the left:

x^2-7x-47-(5x-2)=0

We get rid of parentheses

x^2-7x-5x+2-47=0

We add all the numbers together, and all the variables

x^2-12x-45=0

a = 1; b = -12; c = -45;
Δ = b2-4ac
Δ = -122-4·1·(-45)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-18}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+18}{2*1}=\frac{30}{2}
=15
$