(x+6)(5-x)=-2(5-x)(7x+8)

Solution for (x+6)(5-x)=-2(5-x)(7x+8) equation:

(x+6)(5-x)=-2(5-x)(7x+8)

We move all terms to the left:

(x+6)(5-x)-(-2(5-x)(7x+8))=0

We add all the numbers together, and all the variables

(x+6)(-1x+5)-(-2(-1x+5)(7x+8))=0

We multiply parentheses ..

(-1x^2+5x-6x+30)-(-2(-1x+5)(7x+8))=0


We calculate terms in parentheses: -(-2(-1x+5)(7x+8)), so:

-2(-1x+5)(7x+8)

We multiply parentheses ..

-2(-7x^2-8x+35x+40)

We multiply parentheses

14x^2+16x-70x-80

We add all the numbers together, and all the variables

14x^2-54x-80

Back to the equation:

-(14x^2-54x-80)


We get rid of parentheses

-1x^2-14x^2+5x-6x+54x+30+80=0

We add all the numbers together, and all the variables

-15x^2+53x+110=0

a = -15; b = 53; c = +110;
Δ = b2-4ac
Δ = 532-4·(-15)·110
Δ = 9409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9409}=97$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-97}{2*-15}=\frac{-150}{-30}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+97}{2*-15}=\frac{44}{-30}
=-1+7/15
$