55-3x=(10x+13)(8x+12)

Solution for 55-3x=(10x+13)(8x+12) equation:

55-3x=(10x+13)(8x+12)

We move all terms to the left:

55-3x-((10x+13)(8x+12))=0

We multiply parentheses ..

-((+80x^2+120x+104x+156))-3x+55=0


We calculate terms in parentheses: -((+80x^2+120x+104x+156)), so:

(+80x^2+120x+104x+156)

We get rid of parentheses

80x^2+120x+104x+156

We add all the numbers together, and all the variables

80x^2+224x+156

Back to the equation:

-(80x^2+224x+156)


We add all the numbers together, and all the variables

-3x-(80x^2+224x+156)+55=0

We get rid of parentheses

-80x^2-3x-224x-156+55=0

We add all the numbers together, and all the variables

-80x^2-227x-101=0

a = -80; b = -227; c = -101;
Δ = b2-4ac
Δ = -2272-4·(-80)·(-101)
Δ = 19209
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{-(-227)-\sqrt{19209}}{2*-80}=\frac{227-\sqrt{19209}}{-160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-227)+\sqrt{19209}}{2*-80}=\frac{227+\sqrt{19209}}{-160}
$