X^2-2x-37=7x-1

Solution for X^2-2x-37=7x-1 equation:

X^2-2X-37=7X-1

We move all terms to the left:

X^2-2X-37-(7X-1)=0

We get rid of parentheses

X^2-2X-7X+1-37=0

We add all the numbers together, and all the variables

X^2-9X-36=0

a = 1; b = -9; c = -36;
Δ = b2-4ac
Δ = -92-4·1·(-36)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*1}=\frac{-6}{2}
=-3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*1}=\frac{24}{2}
=12
$