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

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



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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(7.5(3x+3.5)x)+24=0



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

7.5(3x+3.5)x

We multiply parentheses

21x^2+24.5x

Back to the equation:

-(21x^2+24.5x)



We get rid of parentheses

-21x^2-24.5x+24=0

a = -21; b = -24.5; c = +24;
Δ = b2-4ac
Δ = -24.52-4·(-21)·24
Δ = 2616.25
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{-(-24.5)-\sqrt{2616.25}}{2*-21}=\frac{24.5-\sqrt{2616.25}}{-42}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24.5)+\sqrt{2616.25}}{2*-21}=\frac{24.5+\sqrt{2616.25}}{-42}
$

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