(0.25+x)(0.4+x)=0.2

Solution for (0.25+x)(0.4+x)=0.2 equation:

(0.25+x)(0.4+x)=0.2

We move all terms to the left:

(0.25+x)(0.4+x)-(0.2)=0

We add all the numbers together, and all the variables

(x+0.25)(x+0.4)-(0.2)=0

We add all the numbers together, and all the variables

(x+0.25)(x+0.4)-0.2=0

We multiply parentheses ..

(+x^2+0.4x+0.25x+0.1)-0.2=0

We get rid of parentheses

x^2+0.4x+0.25x+0.1-0.2=0

We add all the numbers together, and all the variables

x^2+0.65x-0.1=0

a = 1; b = 0.65; c = -0.1;
Δ = b2-4ac
Δ = 0.652-4·1·(-0.1)
Δ = 0.8225
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{-(0.65)-\sqrt{0.8225}}{2*1}=\frac{-0.65-\sqrt{0.8225}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.65)+\sqrt{0.8225}}{2*1}=\frac{-0.65+\sqrt{0.8225}}{2}
$