0.07(1.08-2x)(0.6-3x)=(0.34+2x)(0.34+2x)

Solution for 0.07(1.08-2x)(0.6-3x)=(0.34+2x)(0.34+2x) equation:

0.07(1.08-2x)(0.6-3x)=(0.34+2x)(0.34+2x)

We move all terms to the left:

0.07(1.08-2x)(0.6-3x)-((0.34+2x)(0.34+2x))=0

We add all the numbers together, and all the variables

0.07(-2x+1.08)(-3x+0.6)-((2x+0.34)(2x+0.34))=0

We multiply parentheses ..

0.07(+6x^2-1.2x-3.24x+0.648)-((2x+0.34)(2x+0.34))=0


We calculate terms in parentheses: -((2x+0.34)(2x+0.34)), so:

(2x+0.34)(2x+0.34)

We multiply parentheses ..

(+4x^2+0.68x+0.68x+0.1156)

We get rid of parentheses

4x^2+0.68x+0.68x+0.1156

We add all the numbers together, and all the variables

4x^2+1.36x+0.1156

Back to the equation:

-(4x^2+1.36x+0.1156)


We multiply parentheses

0.42x^2-0.07x-0.21x-(4x^2+1.36x+0.1156)+0.04536=0

We get rid of parentheses

0.42x^2-4x^2-0.07x-0.21x-1.36x-0.1156+0.04536=0

We add all the numbers together, and all the variables

-3.58x^2-1.64x-0.07024=0

a = -3.58; b = -1.64; c = -0.07024;
Δ = b2-4ac
Δ = -1.642-4·(-3.58)·(-0.07024)
Δ = 1.6837632
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{-(-1.64)-\sqrt{1.6837632}}{2*-3.58}=\frac{1.64-\sqrt{1.6837632}}{-7.16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.64)+\sqrt{1.6837632}}{2*-3.58}=\frac{1.64+\sqrt{1.6837632}}{-7.16}
$