-x(4x+2)+3=5(-x-1)

Solution for -x(4x+2)+3=5(-x-1) equation:

-x(4x+2)+3=5(-x-1)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -(5(-1x-1)), so:

5(-1x-1)

We multiply parentheses

-5x-5

Back to the equation:

-(-5x-5)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -4; b = 3; c = +8;
Δ = b2-4ac
Δ = 32-4·(-4)·8
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{-(3)-\sqrt{137}}{2*-4}=\frac{-3-\sqrt{137}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{137}}{2*-4}=\frac{-3+\sqrt{137}}{-8}
$