3.8x(-9-9.7x)=2.6+13.3x

Solution for 3.8x(-9-9.7x)=2.6+13.3x equation:

3.8x(-9-9.7x)=2.6+13.3x

We move all terms to the left:

3.8x(-9-9.7x)-(2.6+13.3x)=0

We add all the numbers together, and all the variables

3.8x(-9.7x-9)-(13.3x+2.6)=0

We multiply parentheses

-27x^2-27x-(13.3x+2.6)=0

We get rid of parentheses

-27x^2-27x-13.3x-2.6=0

We add all the numbers together, and all the variables

-27x^2-40.3x-2.6=0

a = -27; b = -40.3; c = -2.6;
Δ = b2-4ac
Δ = -40.32-4·(-27)·(-2.6)
Δ = 1343.29
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{-(-40.3)-\sqrt{1343.29}}{2*-27}=\frac{40.3-\sqrt{1343.29}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40.3)+\sqrt{1343.29}}{2*-27}=\frac{40.3+\sqrt{1343.29}}{-54}
$