-4x(2x+5)=2(-x-9)-6

Solution for -4x(2x+5)=2(-x-9)-6 equation:

-4x(2x+5)=2(-x-9)-6

We move all terms to the left:

-4x(2x+5)-(2(-x-9)-6)=0

We add all the numbers together, and all the variables

-4x(2x+5)-(2(-1x-9)-6)=0

We multiply parentheses

-8x^2-20x-(2(-1x-9)-6)=0


We calculate terms in parentheses: -(2(-1x-9)-6), so:

2(-1x-9)-6

We multiply parentheses

-2x-18-6

We add all the numbers together, and all the variables

-2x-24

Back to the equation:

-(-2x-24)


We get rid of parentheses

-8x^2-20x+2x+24=0

We add all the numbers together, and all the variables

-8x^2-18x+24=0

a = -8; b = -18; c = +24;
Δ = b2-4ac
Δ = -182-4·(-8)·24
Δ = 1092
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1092}=\sqrt{4*273}=\sqrt{4}*\sqrt{273}=2\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{273}}{2*-8}=\frac{18-2\sqrt{273}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{273}}{2*-8}=\frac{18+2\sqrt{273}}{-16}
$