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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

(x+3)+(x-4)-((-1x)(x+5)+6)=0

We get rid of parentheses

x+x-((-1x)(x+5)+6)+3-4=0

We multiply parentheses ..

-((-1x^2-5x)+6)+x+x+3-4=0


We calculate terms in parentheses: -((-1x^2-5x)+6), so:

(-1x^2-5x)+6

We get rid of parentheses

-1x^2-5x+6

Back to the equation:

-(-1x^2-5x+6)


We add all the numbers together, and all the variables

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

We get rid of parentheses

1x^2+5x+2x-6-1=0

We add all the numbers together, and all the variables

x^2+7x-7=0

a = 1; b = 7; c = -7;
Δ = b2-4ac
Δ = 72-4·1·(-7)
Δ = 77
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{-(7)-\sqrt{77}}{2*1}=\frac{-7-\sqrt{77}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{77}}{2*1}=\frac{-7+\sqrt{77}}{2}
$