5x(2x-1)-2(3x+3)=6+7(x+4)

Solution for 5x(2x-1)-2(3x+3)=6+7(x+4) equation:

5x(2x-1)-2(3x+3)=6+7(x+4)

We move all terms to the left:

5x(2x-1)-2(3x+3)-(6+7(x+4))=0

We multiply parentheses

10x^2-5x-6x-(6+7(x+4))-6=0


We calculate terms in parentheses: -(6+7(x+4)), so:

6+7(x+4)

determiningTheFunctionDomain
7(x+4)+6

We multiply parentheses

7x+28+6

We add all the numbers together, and all the variables

7x+34

Back to the equation:

-(7x+34)


We add all the numbers together, and all the variables

10x^2-11x-(7x+34)-6=0

We get rid of parentheses

10x^2-11x-7x-34-6=0

We add all the numbers together, and all the variables

10x^2-18x-40=0

a = 10; b = -18; c = -40;
Δ = b2-4ac
Δ = -182-4·10·(-40)
Δ = 1924
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:

$\sqrt{\Delta}=\sqrt{1924}=\sqrt{4*481}=\sqrt{4}*\sqrt{481}=2\sqrt{481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{481}}{2*10}=\frac{18-2\sqrt{481}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{481}}{2*10}=\frac{18+2\sqrt{481}}{20}
$