13.76+.12x(x+3)=14.51+.07x

Solution for 13.76+.12x(x+3)=14.51+.07x equation:

13.76+.12x(x+3)=14.51+.07x

We move all terms to the left:

13.76+.12x(x+3)-(14.51+.07x)=0

We add all the numbers together, and all the variables

.12x(x+3)-(.07x+14.51)+13.76=0

We multiply parentheses

x^2+3x-(.07x+14.51)+13.76=0

We get rid of parentheses

x^2+3x-.07x-14.51+13.76=0

We add all the numbers together, and all the variables

x^2+2.93x-0.75=0

a = 1; b = 2.93; c = -0.75;
Δ = b2-4ac
Δ = 2.932-4·1·(-0.75)
Δ = 11.5849
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{-(2.93)-\sqrt{11.5849}}{2*1}=\frac{-2.93-\sqrt{11.5849}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.93)+\sqrt{11.5849}}{2*1}=\frac{-2.93+\sqrt{11.5849}}{2}
$