3.5x-13+27=3.5x(x+4)

Solution for 3.5x-13+27=3.5x(x+4) equation:

3.5x-13+27=3.5x(x+4)

We move all terms to the left:

3.5x-13+27-(3.5x(x+4))=0

We add all the numbers together, and all the variables

3.5x-(3.5x(x+4))+14=0


We calculate terms in parentheses: -(3.5x(x+4)), so:

3.5x(x+4)

We multiply parentheses

3x^2+12x

Back to the equation:

-(3x^2+12x)


We get rid of parentheses

-3x^2+3.5x-12x+14=0

We add all the numbers together, and all the variables

-3x^2-8.5x+14=0

a = -3; b = -8.5; c = +14;
Δ = b2-4ac
Δ = -8.52-4·(-3)·14
Δ = 240.25
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{-(-8.5)-\sqrt{240.25}}{2*-3}=\frac{8.5-\sqrt{240.25}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8.5)+\sqrt{240.25}}{2*-3}=\frac{8.5+\sqrt{240.25}}{-6}
$