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

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

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

We move all terms to the left:

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

We multiply parentheses

-3x^2-15x-(7-6x(x+3))=0


We calculate terms in parentheses: -(7-6x(x+3)), so:

7-6x(x+3)

determiningTheFunctionDomain
-6x(x+3)+7

We multiply parentheses

-6x^2-18x+7

Back to the equation:

-(-6x^2-18x+7)


We get rid of parentheses

-3x^2+6x^2+18x-15x-7=0

We add all the numbers together, and all the variables

3x^2+3x-7=0

a = 3; b = 3; c = -7;
Δ = b2-4ac
Δ = 32-4·3·(-7)
Δ = 93
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{-(3)-\sqrt{93}}{2*3}=\frac{-3-\sqrt{93}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{93}}{2*3}=\frac{-3+\sqrt{93}}{6}
$