18-(3x+5)=5x(x-1)-6

Solution for 18-(3x+5)=5x(x-1)-6 equation:

18-(3x+5)=5x(x-1)-6

We move all terms to the left:

18-(3x+5)-(5x(x-1)-6)=0

We get rid of parentheses

-3x-(5x(x-1)-6)-5+18=0


We calculate terms in parentheses: -(5x(x-1)-6), so:

5x(x-1)-6

We multiply parentheses

5x^2-5x-6

Back to the equation:

-(5x^2-5x-6)


We add all the numbers together, and all the variables

-3x-(5x^2-5x-6)+13=0

We get rid of parentheses

-5x^2-3x+5x+6+13=0

We add all the numbers together, and all the variables

-5x^2+2x+19=0

a = -5; b = 2; c = +19;
Δ = b2-4ac
Δ = 22-4·(-5)·19
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-8\sqrt{6}}{2*-5}=\frac{-2-8\sqrt{6}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8\sqrt{6}}{2*-5}=\frac{-2+8\sqrt{6}}{-10}
$