3(2x^2)+5-3(2x-3x)+21/28=30

Solution for 3(2x^2)+5-3(2x-3x)+21/28=30 equation:

3(2x^2)+5-3(2x-3x)+21/28=30

We move all terms to the left:

3(2x^2)+5-3(2x-3x)+21/28-(30)=0

determiningTheFunctionDomain
32x^2-3(2x-3x)+5-30+21/28=0

We add all the numbers together, and all the variables

32x^2-3(-1x)+5-30+21/28=0

We add all the numbers together, and all the variables

32x^2-3(-1x)-25+21/28=0

We multiply parentheses

32x^2+3x-25+21/28=0

We multiply all the terms by the denominator


32x^2*28+3x*28+21-25*28=0

We add all the numbers together, and all the variables

32x^2*28+3x*28-679=0

Wy multiply elements

896x^2+84x-679=0

a = 896; b = 84; c = -679;
Δ = b2-4ac
Δ = 842-4·896·(-679)
Δ = 2440592
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2440592}=\sqrt{784*3113}=\sqrt{784}*\sqrt{3113}=28\sqrt{3113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-28\sqrt{3113}}{2*896}=\frac{-84-28\sqrt{3113}}{1792}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+28\sqrt{3113}}{2*896}=\frac{-84+28\sqrt{3113}}{1792}
$