4(2x+9)5x=-3

Solution for 4(2x+9)5x=-3 equation:

4(2x+9)5x=-3

We move all terms to the left:

4(2x+9)5x-(-3)=0

We add all the numbers together, and all the variables

4(2x+9)5x+3=0

We multiply parentheses

40x^2+180x+3=0

a = 40; b = 180; c = +3;
Δ = b2-4ac
Δ = 1802-4·40·3
Δ = 31920
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{31920}=\sqrt{16*1995}=\sqrt{16}*\sqrt{1995}=4\sqrt{1995}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-4\sqrt{1995}}{2*40}=\frac{-180-4\sqrt{1995}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+4\sqrt{1995}}{2*40}=\frac{-180+4\sqrt{1995}}{80}
$