0.5x+0.2(50)=0.4x(x+30)

Solution for 0.5x+0.2(50)=0.4x(x+30) equation:

0.5x+0.2(50)=0.4x(x+30)

We move all terms to the left:

0.5x+0.2(50)-(0.4x(x+30))=0

We add all the numbers together, and all the variables

0.5x-(0.4x(x+30))+0.25=0


We calculate terms in parentheses: -(0.4x(x+30)), so:

0.4x(x+30)

We multiply parentheses

0x^2+0x

We add all the numbers together, and all the variables

x^2+x

Back to the equation:

-(x^2+x)


We get rid of parentheses

-x^2+0.5x-x+0.25=0

We add all the numbers together, and all the variables

-1x^2-0.5x+0.25=0

a = -1; b = -0.5; c = +0.25;
Δ = b2-4ac
Δ = -0.52-4·(-1)·0.25
Δ = 1.25
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{-(-0.5)-\sqrt{1.25}}{2*-1}=\frac{0.5-\sqrt{1.25}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{1.25}}{2*-1}=\frac{0.5+\sqrt{1.25}}{-2}
$