(0.050+x)(0.040+x)=(0.045-x)(0.40-x)*0.517

Solution for (0.050+x)(0.040+x)=(0.045-x)(0.40-x)*0.517 equation:

(0.050+x)(0.040+x)=(0.045-x)(0.40-x)*0.517

We move all terms to the left:

(0.050+x)(0.040+x)-((0.045-x)(0.40-x)*0.517)=0

We add all the numbers together, and all the variables

(x+0.05)(x+0.04)-((-1x+0.045)(-1x+0.4)*0.517)=0

We multiply parentheses ..

(+x^2+0.04x+0.05x+0.002)-((-1x+0.045)(-1x+0.4)*0.517)=0


We calculate terms in parentheses: -((-1x+0.045)(-1x+0.4)*0.517), so:

(-1x+0.045)(-1x+0.4)*0.517

We multiply parentheses ..

(+x^2-0.4x-0.045x+0.018)*0.517

We multiply parentheses

0.517x^2+0x+0x+0.009306

We add all the numbers together, and all the variables

0.517x^2+2x+0.009306

Back to the equation:

-(0.517x^2+2x+0.009306)


We get rid of parentheses

x^2-0.517x^2+0.04x+0.05x-2x+0.002-0.009306=0

We add all the numbers together, and all the variables

0.483x^2-1.91x-0.007306=0

a = 0.483; b = -1.91; c = -0.007306;
Δ = b2-4ac
Δ = -1.912-4·0.483·(-0.007306)
Δ = 3.662215192
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{-(-1.91)-\sqrt{3.662215192}}{2*0.483}=\frac{1.91-\sqrt{3.662215192}}{0.966}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.91)+\sqrt{3.662215192}}{2*0.483}=\frac{1.91+\sqrt{3.662215192}}{0.966}
$