X^2-47=10x-8

Solution for X^2-47=10x-8 equation:

X^2-47=10X-8

We move all terms to the left:

X^2-47-(10X-8)=0

We get rid of parentheses

X^2-10X+8-47=0

We add all the numbers together, and all the variables

X^2-10X-39=0

a = 1; b = -10; c = -39;
Δ = b2-4ac
Δ = -102-4·1·(-39)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-16}{2*1}=\frac{-6}{2}
=-3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+16}{2*1}=\frac{26}{2}
=13
$