(0.105+x)(0.105+x)=(0.0784)(0.139-x)

Solution for (0.105+x)(0.105+x)=(0.0784)(0.139-x) equation:

(0.105+x)(0.105+x)=(0.0784)(0.139-x)

We move all terms to the left:

(0.105+x)(0.105+x)-((0.0784)(0.139-x))=0

We add all the numbers together, and all the variables

(x+0.105)(x+0.105)-((0.0784)(-1x+0.139))=0

We multiply parentheses ..

(+x^2+0.105x+0.105x+0.011025)-((0.0784)(-1x+0.139))=0


We calculate terms in parentheses: -((0.0784)(-1x+0.139)), so:

(0.0784)(-1x+0.139)

We multiply parentheses ..

(-0.0784x+0.0108976)

We get rid of parentheses

-0.0784x+0.0108976

Back to the equation:

-(-0.0784x+0.0108976)


We get rid of parentheses

x^2+0.105x+0.105x+0.0784x+0.011025-0.0108976=0

We add all the numbers together, and all the variables

x^2+0.2884x+0.0001274=0

a = 1; b = 0.2884; c = +0.0001274;
Δ = b2-4ac
Δ = 0.28842-4·1·0.0001274
Δ = 0.08266496
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{-(0.2884)-\sqrt{0.08266496}}{2*1}=\frac{-0.2884-\sqrt{0.08266496}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.2884)+\sqrt{0.08266496}}{2*1}=\frac{-0.2884+\sqrt{0.08266496}}{2}
$