(4x-24.6)*(x+11.3)=180

Solution for (4x-24.6)*(x+11.3)=180 equation:

(4x-24.6)(x+11.3)=180

We move all terms to the left:

(4x-24.6)(x+11.3)-(180)=0

We multiply parentheses ..

(+4x^2+45.2x-24.6x-277.98)-180=0

We get rid of parentheses

4x^2+45.2x-24.6x-277.98-180=0

We add all the numbers together, and all the variables

4x^2+20.6x-457.98=0

a = 4; b = 20.6; c = -457.98;
Δ = b2-4ac
Δ = 20.62-4·4·(-457.98)
Δ = 7752.04
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{-(20.6)-\sqrt{7752.04}}{2*4}=\frac{-20.6-\sqrt{7752.04}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20.6)+\sqrt{7752.04}}{2*4}=\frac{-20.6+\sqrt{7752.04}}{8}
$