(0.6-x)(1.18-x)=3.0(0.8+x)(0.1+x)

Solution for (0.6-x)(1.18-x)=3.0(0.8+x)(0.1+x) equation:

(0.6-x)(1.18-x)=3.0(0.8+x)(0.1+x)

We move all terms to the left:

(0.6-x)(1.18-x)-(3.0(0.8+x)(0.1+x))=0

We add all the numbers together, and all the variables

(-1x+0.6)(-1x+1.18)-(3.0(x+0.8)(x+0.1))=0

We multiply parentheses ..

(+x^2-1.18x-0.6x+0.708)-(3.0(x+0.8)(x+0.1))=0


We calculate terms in parentheses: -(3.0(x+0.8)(x+0.1)), so:

3.0(x+0.8)(x+0.1)

We multiply parentheses ..

3.0(+x^2+0.1x+0.8x+0.08)

We multiply parentheses

3x^2+0x+0x+0.24

We add all the numbers together, and all the variables

3x^2+2x+0.24

Back to the equation:

-(3x^2+2x+0.24)


We get rid of parentheses

x^2-3x^2-1.18x-0.6x-2x+0.708-0.24=0

We add all the numbers together, and all the variables

-2x^2-3.78x+0.468=0

a = -2; b = -3.78; c = +0.468;
Δ = b2-4ac
Δ = -3.782-4·(-2)·0.468
Δ = 18.0324
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{-(-3.78)-\sqrt{18.0324}}{2*-2}=\frac{3.78-\sqrt{18.0324}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3.78)+\sqrt{18.0324}}{2*-2}=\frac{3.78+\sqrt{18.0324}}{-4}
$