29.5-5.5x=7.5x(3x+3.5)

Solution for 29.5-5.5x=7.5x(3x+3.5) equation:

29.5-5.5x=7.5x(3x+3.5)

We move all terms to the left:

29.5-5.5x-(7.5x(3x+3.5))=0


We calculate terms in parentheses: -(7.5x(3x+3.5)), so:

7.5x(3x+3.5)

We multiply parentheses

21x^2+24.5x

Back to the equation:

-(21x^2+24.5x)


We get rid of parentheses

-21x^2-5.5x-24.5x+29.5=0

We add all the numbers together, and all the variables

-21x^2-30x+29.5=0

a = -21; b = -30; c = +29.5;
Δ = b2-4ac
Δ = -302-4·(-21)·29.5
Δ = 3378
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{-(-30)-\sqrt{3378}}{2*-21}=\frac{30-\sqrt{3378}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+\sqrt{3378}}{2*-21}=\frac{30+\sqrt{3378}}{-42}
$