7+8-3x(2x-1x)=9+3(4x-3x)-2

Solution for 7+8-3x(2x-1x)=9+3(4x-3x)-2 equation:

7+8-3x(2x-1x)=9+3(4x-3x)-2

We move all terms to the left:

7+8-3x(2x-1x)-(9+3(4x-3x)-2)=0

We add all the numbers together, and all the variables

-3x(+x)-(9+3(+x)-2)+7+8=0

We add all the numbers together, and all the variables

-3x(+x)-(9+3(+x)-2)+15=0

We multiply parentheses

-3x^2-(9+3(+x)-2)+15=0


We calculate terms in parentheses: -(9+3(+x)-2), so:

9+3(+x)-2

determiningTheFunctionDomain
3(+x)+9-2

We add all the numbers together, and all the variables

3(+x)+7

We multiply parentheses

3x+7

Back to the equation:

-(3x+7)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2-3x+8=0

a = -3; b = -3; c = +8;
Δ = b2-4ac
Δ = -32-4·(-3)·8
Δ = 105
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{105}}{2*-3}=\frac{3-\sqrt{105}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{105}}{2*-3}=\frac{3+\sqrt{105}}{-6}
$