1.30x-(x-2.30)(3.10x-5.40)-2.88=4.60-(3.10-1.20)(x-5.30)-4.30x

Solution for 1.30x-(x-2.30)(3.10x-5.40)-2.88=4.60-(3.10-1.20)(x-5.30)-4.30x equation:

1.30x-(x-2.30)(3.10x-5.40)-2.88=4.60-(3.10-1.20)(x-5.30)-4.30x

We move all terms to the left:

1.30x-(x-2.30)(3.10x-5.40)-2.88-(4.60-(3.10-1.20)(x-5.30)-4.30x)=0

We add all the numbers together, and all the variables

1.30x-(x-2.3)(3.10x-5.4)-(4.60-(1.9)(x-5.3)-4.30x)-2.88=0

We multiply parentheses ..

-(+3x^2-5.4x-6.9x+12.42)+1.30x-(4.60-(1.9)(x-5.3)-4.30x)-2.88=0


We calculate terms in parentheses: -(4.60-(1.9)(x-5.3)-4.30x), so:

4.60-(1.9)(x-5.3)-4.30x

determiningTheFunctionDomain
-(1.9)(x-5.3)-4.30x+4.60

We add all the numbers together, and all the variables

-4.3x-(1.9)(x-5.3)+4.6

We multiply parentheses ..

-4.3x-(+1.9x-10.07)+4.6

We add all the numbers together, and all the variables

-4.3x-(1.9x-10.07)+4.6

We get rid of parentheses

-4.3x-1.9x+10.07+4.6

We add all the numbers together, and all the variables

-6.2x+14.67

Back to the equation:

-(-6.2x+14.67)


We get rid of parentheses

-3x^2+5.4x+6.9x+1.30x+6.2x-12.42-14.67-2.88=0

We add all the numbers together, and all the variables

-3x^2+19.8x-29.97=0

a = -3; b = 19.8; c = -29.97;
Δ = b2-4ac
Δ = 19.82-4·(-3)·(-29.97)
Δ = 32.4
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{-(19.8)-\sqrt{32.4}}{2*-3}=\frac{-19.8-\sqrt{32.4}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19.8)+\sqrt{32.4}}{2*-3}=\frac{-19.8+\sqrt{32.4}}{-6}
$