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

Solution for 7(x+4)=2(x-3)(5+x)=2/3(x-6) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

7x-(2(x-3)(x+5))+28=0

We multiply parentheses ..

-(2(+x^2+5x-3x-15))+7x+28=0


We calculate terms in parentheses: -(2(+x^2+5x-3x-15)), so:

2(+x^2+5x-3x-15)

We multiply parentheses

2x^2+10x-6x-30

We add all the numbers together, and all the variables

2x^2+4x-30

Back to the equation:

-(2x^2+4x-30)


We add all the numbers together, and all the variables

7x-(2x^2+4x-30)+28=0

We get rid of parentheses

-2x^2+7x-4x+30+28=0

We add all the numbers together, and all the variables

-2x^2+3x+58=0

a = -2; b = 3; c = +58;
Δ = b2-4ac
Δ = 32-4·(-2)·58
Δ = 473
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{473}}{2*-2}=\frac{-3-\sqrt{473}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{473}}{2*-2}=\frac{-3+\sqrt{473}}{-4}
$