5x(18x+45)=-24

Solution for 5x(18x+45)=-24 equation:

5x(18x+45)=-24

We move all terms to the left:

5x(18x+45)-(-24)=0

We add all the numbers together, and all the variables

5x(18x+45)+24=0

We multiply parentheses

90x^2+225x+24=0

a = 90; b = 225; c = +24;
Δ = b2-4ac
Δ = 2252-4·90·24
Δ = 41985
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:

$\sqrt{\Delta}=\sqrt{41985}=\sqrt{9*4665}=\sqrt{9}*\sqrt{4665}=3\sqrt{4665}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(225)-3\sqrt{4665}}{2*90}=\frac{-225-3\sqrt{4665}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(225)+3\sqrt{4665}}{2*90}=\frac{-225+3\sqrt{4665}}{180}
$