(5x+1)=(18x+11)x=

Solution for (5x+1)=(18x+11)x= equation:

(5x+1)=(18x+11)x=

We move all terms to the left:

(5x+1)-((18x+11)x)=0

We get rid of parentheses

5x-((18x+11)x)+1=0


We calculate terms in parentheses: -((18x+11)x), so:

(18x+11)x

We multiply parentheses

18x^2+11x

Back to the equation:

-(18x^2+11x)


We get rid of parentheses

-18x^2+5x-11x+1=0

We add all the numbers together, and all the variables

-18x^2-6x+1=0

a = -18; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·(-18)·1
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{3}}{2*-18}=\frac{6-6\sqrt{3}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{3}}{2*-18}=\frac{6+6\sqrt{3}}{-36}
$