180=(6x+7)(4x+9)+(3x+8)

Solution for 180=(6x+7)(4x+9)+(3x+8) equation:

180=(6x+7)(4x+9)+(3x+8)

We move all terms to the left:

180-((6x+7)(4x+9)+(3x+8))=0

We multiply parentheses ..

-((+24x^2+54x+28x+63)+(3x+8))+180=0


We calculate terms in parentheses: -((+24x^2+54x+28x+63)+(3x+8)), so:

(+24x^2+54x+28x+63)+(3x+8)

We get rid of parentheses

24x^2+54x+28x+3x+63+8

We add all the numbers together, and all the variables

24x^2+85x+71

Back to the equation:

-(24x^2+85x+71)


We get rid of parentheses

-24x^2-85x-71+180=0

We add all the numbers together, and all the variables

-24x^2-85x+109=0

a = -24; b = -85; c = +109;
Δ = b2-4ac
Δ = -852-4·(-24)·109
Δ = 17689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17689}=133$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-85)-133}{2*-24}=\frac{-48}{-48}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+133}{2*-24}=\frac{218}{-48}
=-4+13/24
$