6x2-4x-5=x2-3x-1

Solution for 6x2-4x-5=x2-3x-1 equation:

6x^2-4x-5=x2-3x-1

We move all terms to the left:

6x^2-4x-5-(x2-3x-1)=0

We add all the numbers together, and all the variables

6x^2-(+x^2-3x-1)-4x-5=0

We get rid of parentheses

6x^2-x^2+3x-4x+1-5=0

We add all the numbers together, and all the variables

5x^2-1x-4=0

a = 5; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·5·(-4)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*5}=\frac{-8}{10}
=-4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*5}=\frac{10}{10}
=1
$