7x(3x+11)=6-(5-3x)

Solution for 7x(3x+11)=6-(5-3x) equation:

7x(3x+11)=6-(5-3x)

We move all terms to the left:

7x(3x+11)-(6-(5-3x))=0

We add all the numbers together, and all the variables

7x(3x+11)-(6-(-3x+5))=0

We multiply parentheses

21x^2+77x-(6-(-3x+5))=0


We calculate terms in parentheses: -(6-(-3x+5)), so:

6-(-3x+5)

determiningTheFunctionDomain
-(-3x+5)+6

We get rid of parentheses

3x-5+6

We add all the numbers together, and all the variables

3x+1

Back to the equation:

-(3x+1)


We get rid of parentheses

21x^2+77x-3x-1=0

We add all the numbers together, and all the variables

21x^2+74x-1=0

a = 21; b = 74; c = -1;
Δ = b2-4ac
Δ = 742-4·21·(-1)
Δ = 5560
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:

$\sqrt{\Delta}=\sqrt{5560}=\sqrt{4*1390}=\sqrt{4}*\sqrt{1390}=2\sqrt{1390}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(74)-2\sqrt{1390}}{2*21}=\frac{-74-2\sqrt{1390}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(74)+2\sqrt{1390}}{2*21}=\frac{-74+2\sqrt{1390}}{42}
$