56=(x-7)+(x+5)+(x^2-3x)+(3x-4)

Solution for 56=(x-7)+(x+5)+(x^2-3x)+(3x-4) equation:

56=(x-7)+(x+5)+(x^2-3x)+(3x-4)

We move all terms to the left:

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


We calculate terms in parentheses: -((x-7)+(x+5)+(x^2-3x)+(3x-4)), so:

(x-7)+(x+5)+(x^2-3x)+(3x-4)

We get rid of parentheses

x^2+x+x-3x+3x-7+5-4

We add all the numbers together, and all the variables

x^2+2x-6

Back to the equation:

-(x^2+2x-6)


We get rid of parentheses

-x^2-2x+6+56=0

We add all the numbers together, and all the variables

-1x^2-2x+62=0

a = -1; b = -2; c = +62;
Δ = b2-4ac
Δ = -22-4·(-1)·62
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{7}}{2*-1}=\frac{2-6\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{7}}{2*-1}=\frac{2+6\sqrt{7}}{-2}
$