.1x(x+13)=-2(6-x)

Solution for .1x(x+13)=-2(6-x) equation:

.1x(x+13)=-2(6-x)

We move all terms to the left:

.1x(x+13)-(-2(6-x))=0

We add all the numbers together, and all the variables

.1x(x+13)-(-2(-1x+6))=0

We multiply parentheses

x^2+13x-(-2(-1x+6))=0


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

-2(-1x+6)

We multiply parentheses

2x-12

Back to the equation:

-(2x-12)


We get rid of parentheses

x^2+13x-2x+12=0

We add all the numbers together, and all the variables

x^2+11x+12=0

a = 1; b = 11; c = +12;
Δ = b2-4ac
Δ = 112-4·1·12
Δ = 73
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{-(11)-\sqrt{73}}{2*1}=\frac{-11-\sqrt{73}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{73}}{2*1}=\frac{-11+\sqrt{73}}{2}
$