13(2)=(x-7)+x(2)

Solution for 13(2)=(x-7)+x(2) equation:

13(2)=(x-7)+x(2)

We move all terms to the left:

13(2)-((x-7)+x(2))=0


We calculate terms in parentheses: -((x-7)+x2), so:

(x-7)+x2

We add all the numbers together, and all the variables

x^2+(x-7)

We get rid of parentheses

x^2+x-7

Back to the equation:

-(x^2+x-7)


We get rid of parentheses

-x^2-x+7+132=0

We add all the numbers together, and all the variables

-1x^2-1x+139=0

a = -1; b = -1; c = +139;
Δ = b2-4ac
Δ = -12-4·(-1)·139
Δ = 557
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{-(-1)-\sqrt{557}}{2*-1}=\frac{1-\sqrt{557}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{557}}{2*-1}=\frac{1+\sqrt{557}}{-2}
$