13.56+0.07x(x+3)=14.31-0.11x

Solution for 13.56+0.07x(x+3)=14.31-0.11x equation:

13.56+0.07x(x+3)=14.31-0.11x

We move all terms to the left:

13.56+0.07x(x+3)-(14.31-0.11x)=0

We add all the numbers together, and all the variables

0.07x(x+3)-(-0.11x+14.31)+13.56=0

We multiply parentheses

0x^2+0x-(-0.11x+14.31)+13.56=0

We get rid of parentheses

0x^2+0x+0.11x-14.31+13.56=0

We add all the numbers together, and all the variables

x^2+1.11x-0.75=0

a = 1; b = 1.11; c = -0.75;
Δ = b2-4ac
Δ = 1.112-4·1·(-0.75)
Δ = 4.2321
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{-(1.11)-\sqrt{4.2321}}{2*1}=\frac{-1.11-\sqrt{4.2321}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.11)+\sqrt{4.2321}}{2*1}=\frac{-1.11+\sqrt{4.2321}}{2}
$