3x^2-5x-1=4x^2+7x-1

Solution for 3x^2-5x-1=4x^2+7x-1 equation:

3x^2-5x-1=4x^2+7x-1

We move all terms to the left:

3x^2-5x-1-(4x^2+7x-1)=0

We get rid of parentheses

3x^2-4x^2-5x-7x+1-1=0

We add all the numbers together, and all the variables

-1x^2-12x=0

a = -1; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-1)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-1}=\frac{24}{-2}
=-12
$