0.06x(x-5)+0.8(x-6)=0.2x-1.8

Solution for 0.06x(x-5)+0.8(x-6)=0.2x-1.8 equation:

0.06x(x-5)+0.8(x-6)=0.2x-1.8

We move all terms to the left:

0.06x(x-5)+0.8(x-6)-(0.2x-1.8)=0

We multiply parentheses

0x^2+0x+0.8x-(0.2x-1.8)-4.8=0

We get rid of parentheses

0x^2+0x+0.8x-0.2x+1.8-4.8=0

We add all the numbers together, and all the variables

x^2+1.6x-3=0

a = 1; b = 1.6; c = -3;
Δ = b2-4ac
Δ = 1.62-4·1·(-3)
Δ = 14.56
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{-(1.6)-\sqrt{14.56}}{2*1}=\frac{-1.6-\sqrt{14.56}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.6)+\sqrt{14.56}}{2*1}=\frac{-1.6+\sqrt{14.56}}{2}
$