3x(5x-9)=7-4(x+1)

Solution for 3x(5x-9)=7-4(x+1) equation:

3x(5x-9)=7-4(x+1)

We move all terms to the left:

3x(5x-9)-(7-4(x+1))=0

We multiply parentheses

15x^2-27x-(7-4(x+1))=0


We calculate terms in parentheses: -(7-4(x+1)), so:

7-4(x+1)

determiningTheFunctionDomain
-4(x+1)+7

We multiply parentheses

-4x-4+7

We add all the numbers together, and all the variables

-4x+3

Back to the equation:

-(-4x+3)


We get rid of parentheses

15x^2-27x+4x-3=0

We add all the numbers together, and all the variables

15x^2-23x-3=0

a = 15; b = -23; c = -3;
Δ = b2-4ac
Δ = -232-4·15·(-3)
Δ = 709
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{-(-23)-\sqrt{709}}{2*15}=\frac{23-\sqrt{709}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{709}}{2*15}=\frac{23+\sqrt{709}}{30}
$