2x(5x-1)=3(x+11)

Solution for 2x(5x-1)=3(x+11) equation:

2x(5x-1)=3(x+11)

We move all terms to the left:

2x(5x-1)-(3(x+11))=0

We multiply parentheses

10x^2-2x-(3(x+11))=0


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

3(x+11)

We multiply parentheses

3x+33

Back to the equation:

-(3x+33)


We get rid of parentheses

10x^2-2x-3x-33=0

We add all the numbers together, and all the variables

10x^2-5x-33=0

a = 10; b = -5; c = -33;
Δ = b2-4ac
Δ = -52-4·10·(-33)
Δ = 1345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{1345}}{2*10}=\frac{5-\sqrt{1345}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{1345}}{2*10}=\frac{5+\sqrt{1345}}{20}
$