18+(2x-15)x=3(11-5x)

Solution for 18+(2x-15)x=3(11-5x) equation:

18+(2x-15)x=3(11-5x)

We move all terms to the left:

18+(2x-15)x-(3(11-5x))=0

We add all the numbers together, and all the variables

(2x-15)x-(3(-5x+11))+18=0

We multiply parentheses

2x^2-15x-(3(-5x+11))+18=0


We calculate terms in parentheses: -(3(-5x+11)), so:

3(-5x+11)

We multiply parentheses

-15x+33

Back to the equation:

-(-15x+33)


We get rid of parentheses

2x^2-15x+15x-33+18=0

We add all the numbers together, and all the variables

2x^2-15=0

a = 2; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·2·(-15)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*2}=\frac{0-2\sqrt{30}}{4}
=-\frac{2\sqrt{30}}{4}
=-\frac{\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*2}=\frac{0+2\sqrt{30}}{4}
=\frac{2\sqrt{30}}{4}
=\frac{\sqrt{30}}{2}
$