0.3x+1.8=0.4x(x+5)-0.2

Solution for 0.3x+1.8=0.4x(x+5)-0.2 equation:

0.3x+1.8=0.4x(x+5)-0.2

We move all terms to the left:

0.3x+1.8-(0.4x(x+5)-0.2)=0


We calculate terms in parentheses: -(0.4x(x+5)-0.2), so:

0.4x(x+5)-0.2

We multiply parentheses

0x^2+0x-0.2

We add all the numbers together, and all the variables

x^2+x-0.2

Back to the equation:

-(x^2+x-0.2)


We get rid of parentheses

-x^2+0.3x-x+0.2+1.8=0

We add all the numbers together, and all the variables

-1x^2-0.7x+2=0

a = -1; b = -0.7; c = +2;
Δ = b2-4ac
Δ = -0.72-4·(-1)·2
Δ = 8.49
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{-(-0.7)-\sqrt{8.49}}{2*-1}=\frac{0.7-\sqrt{8.49}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.7)+\sqrt{8.49}}{2*-1}=\frac{0.7+\sqrt{8.49}}{-2}
$