7+2(3x-4)=9+5x(-x+3)

Solution for 7+2(3x-4)=9+5x(-x+3) equation:

7+2(3x-4)=9+5x(-x+3)

We move all terms to the left:

7+2(3x-4)-(9+5x(-x+3))=0

We add all the numbers together, and all the variables

2(3x-4)-(9+5x(-1x+3))+7=0

We multiply parentheses

6x-(9+5x(-1x+3))-8+7=0


We calculate terms in parentheses: -(9+5x(-1x+3)), so:

9+5x(-1x+3)

determiningTheFunctionDomain
5x(-1x+3)+9

We multiply parentheses

-5x^2+15x+9

Back to the equation:

-(-5x^2+15x+9)


We add all the numbers together, and all the variables

-(-5x^2+15x+9)+6x-1=0

We get rid of parentheses

5x^2-15x+6x-9-1=0

We add all the numbers together, and all the variables

5x^2-9x-10=0

a = 5; b = -9; c = -10;
Δ = b2-4ac
Δ = -92-4·5·(-10)
Δ = 281
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{-(-9)-\sqrt{281}}{2*5}=\frac{9-\sqrt{281}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{281}}{2*5}=\frac{9+\sqrt{281}}{10}
$