5.5x+6.25(100)=6x(x+100)

Solution for 5.5x+6.25(100)=6x(x+100) equation:

5.5x+6.25(100)=6x(x+100)

We move all terms to the left:

5.5x+6.25(100)-(6x(x+100))=0

We add all the numbers together, and all the variables

5.5x-(6x(x+100))+6.251=0


We calculate terms in parentheses: -(6x(x+100)), so:

6x(x+100)

We multiply parentheses

6x^2+600x

Back to the equation:

-(6x^2+600x)


We get rid of parentheses

-6x^2+5.5x-600x+6.251=0

We add all the numbers together, and all the variables

-6x^2-594.5x+6.251=0

a = -6; b = -594.5; c = +6.251;
Δ = b2-4ac
Δ = -594.52-4·(-6)·6.251
Δ = 353580.274
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{-(-594.5)-\sqrt{353580.274}}{2*-6}=\frac{594.5-\sqrt{353580.274}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-594.5)+\sqrt{353580.274}}{2*-6}=\frac{594.5+\sqrt{353580.274}}{-12}
$