X*x+7x-5=6x+1

Solution for X*x+7x-5=6x+1 equation:

X*X+7X-5=6X+1

We move all terms to the left:

X*X+7X-5-(6X+1)=0

We add all the numbers together, and all the variables

7X+X*X-(6X+1)-5=0

Wy multiply elements

X^2+7X-(6X+1)-5=0

We get rid of parentheses

X^2+7X-6X-1-5=0

We add all the numbers together, and all the variables

X^2+X-6=0

a = 1; b = 1; c = -6;
Δ = b2-4ac
Δ = 12-4·1·(-6)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5}{2*1}=\frac{-6}{2}
=-3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*1}=\frac{4}{2}
=2
$