-6(x+5)+3=-2(x+4)4x

Solution for -6(x+5)+3=-2(x+4)4x equation:

-6(x+5)+3=-2(x+4)4x

We move all terms to the left:

-6(x+5)+3-(-2(x+4)4x)=0

We multiply parentheses

-6x-(-2(x+4)4x)-30+3=0


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

-2(x+4)4x

We multiply parentheses

-8x^2-32x

Back to the equation:

-(-8x^2-32x)


We add all the numbers together, and all the variables

-(-8x^2-32x)-6x-27=0

We get rid of parentheses

8x^2+32x-6x-27=0

We add all the numbers together, and all the variables

8x^2+26x-27=0

a = 8; b = 26; c = -27;
Δ = b2-4ac
Δ = 262-4·8·(-27)
Δ = 1540
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:

$\sqrt{\Delta}=\sqrt{1540}=\sqrt{4*385}=\sqrt{4}*\sqrt{385}=2\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{385}}{2*8}=\frac{-26-2\sqrt{385}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{385}}{2*8}=\frac{-26+2\sqrt{385}}{16}
$