3x-1=-4(x+2);x=-1

Solution for 3x-1=-4(x+2);x=-1 equation:

3x-1=-4(x+2)x=-1

We move all terms to the left:

3x-1-(-4(x+2)x)=0


We calculate terms in parentheses: -(-4(x+2)x), so:

-4(x+2)x

We multiply parentheses

-4x^2-8x

Back to the equation:

-(-4x^2-8x)


We get rid of parentheses

4x^2+8x+3x-1=0

We add all the numbers together, and all the variables

4x^2+11x-1=0

a = 4; b = 11; c = -1;
Δ = b2-4ac
Δ = 112-4·4·(-1)
Δ = 137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{137}}{2*4}=\frac{-11-\sqrt{137}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{137}}{2*4}=\frac{-11+\sqrt{137}}{8}
$