5x(x-3)-(2x+1)=4(3x+2)

Solution for 5x(x-3)-(2x+1)=4(3x+2) equation:

5x(x-3)-(2x+1)=4(3x+2)

We move all terms to the left:

5x(x-3)-(2x+1)-(4(3x+2))=0

We multiply parentheses

5x^2-15x-(2x+1)-(4(3x+2))=0

We get rid of parentheses

5x^2-15x-2x-(4(3x+2))-1=0


We calculate terms in parentheses: -(4(3x+2)), so:

4(3x+2)

We multiply parentheses

12x+8

Back to the equation:

-(12x+8)


We add all the numbers together, and all the variables

5x^2-17x-(12x+8)-1=0

We get rid of parentheses

5x^2-17x-12x-8-1=0

We add all the numbers together, and all the variables

5x^2-29x-9=0

a = 5; b = -29; c = -9;
Δ = b2-4ac
Δ = -292-4·5·(-9)
Δ = 1021
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{-(-29)-\sqrt{1021}}{2*5}=\frac{29-\sqrt{1021}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{1021}}{2*5}=\frac{29+\sqrt{1021}}{10}
$