4+3(5x-18)x=5

Solution for 4+3(5x-18)x=5 equation:

4+3(5x-18)x=5

We move all terms to the left:

4+3(5x-18)x-(5)=0

We add all the numbers together, and all the variables

3(5x-18)x-1=0

We multiply parentheses

15x^2-54x-1=0

a = 15; b = -54; c = -1;
Δ = b2-4ac
Δ = -542-4·15·(-1)
Δ = 2976
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:

$\sqrt{\Delta}=\sqrt{2976}=\sqrt{16*186}=\sqrt{16}*\sqrt{186}=4\sqrt{186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-4\sqrt{186}}{2*15}=\frac{54-4\sqrt{186}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+4\sqrt{186}}{2*15}=\frac{54+4\sqrt{186}}{30}
$