(0.20)(10)=0,05x+0.40x(10-x)

Solution for (0.20)(10)=0,05x+0.40x(10-x) equation:

(0.20)(10)=0.05x+0.40x(10-x)

We move all terms to the left:

(0.20)(10)-(0.05x+0.40x(10-x))=0

We add all the numbers together, and all the variables

-(0.05x+0.40x(-1x+10))+(0.2)10=0

We add all the numbers together, and all the variables

-(0.05x+0.40x(-1x+10))+2=0


We calculate terms in parentheses: -(0.05x+0.40x(-1x+10)), so:

0.05x+0.40x(-1x+10)

We multiply parentheses

0x^2+0.05x+0x

We add all the numbers together, and all the variables

x^2+1.05x

Back to the equation:

-(x^2+1.05x)


We get rid of parentheses

-x^2-1.05x+2=0

We add all the numbers together, and all the variables

-1x^2-1.05x+2=0

a = -1; b = -1.05; c = +2;
Δ = b2-4ac
Δ = -1.052-4·(-1)·2
Δ = 9.1025
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{-(-1.05)-\sqrt{9.1025}}{2*-1}=\frac{1.05-\sqrt{9.1025}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.05)+\sqrt{9.1025}}{2*-1}=\frac{1.05+\sqrt{9.1025}}{-2}
$