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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2+11x+4=0

a = -3; b = 11; c = +4;
Δ = b2-4ac
Δ = 112-4·(-3)·4
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-13}{2*-3}=\frac{-24}{-6}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+13}{2*-3}=\frac{2}{-6}
=-1/3
$