4.24(0.19+x)(0.19+x)=(0.19-x)(0.19-x)

Solution for 4.24(0.19+x)(0.19+x)=(0.19-x)(0.19-x) equation:

4.24(0.19+x)(0.19+x)=(0.19-x)(0.19-x)

We move all terms to the left:

4.24(0.19+x)(0.19+x)-((0.19-x)(0.19-x))=0

We add all the numbers together, and all the variables

4.24(x+0.19)(x+0.19)-((-1x+0.19)(-1x+0.19))=0

We multiply parentheses ..

4.24(+x^2+0.19x+0.19x+0.0361)-((-1x+0.19)(-1x+0.19))=0


We calculate terms in parentheses: -((-1x+0.19)(-1x+0.19)), so:

(-1x+0.19)(-1x+0.19)

We multiply parentheses ..

(+x^2-0.19x-0.19x+0.0361)

We get rid of parentheses

x^2-0.19x-0.19x+0.0361

We add all the numbers together, and all the variables

x^2-0.38x+0.0361

Back to the equation:

-(x^2-0.38x+0.0361)


We multiply parentheses

4.24x^2+0x+0x-(x^2-0.38x+0.0361)+0.153064=0

We get rid of parentheses

4.24x^2-x^2+0x+0x+0.38x-0.0361+0.153064=0

We add all the numbers together, and all the variables

3.24x^2+2.38x+0.116964=0

a = 3.24; b = 2.38; c = +0.116964;
Δ = b2-4ac
Δ = 2.382-4·3.24·0.116964
Δ = 4.14854656
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{-(2.38)-\sqrt{4.14854656}}{2*3.24}=\frac{-2.38-\sqrt{4.14854656}}{6.48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.38)+\sqrt{4.14854656}}{2*3.24}=\frac{-2.38+\sqrt{4.14854656}}{6.48}
$