0.2(x-4)(x+6)=5

Solution for 0.2(x-4)(x+6)=5 equation:

0.2(x-4)(x+6)=5

We move all terms to the left:

0.2(x-4)(x+6)-(5)=0

We multiply parentheses ..

0.2(+x^2+6x-4x-24)-5=0

We multiply parentheses

0.2x^2+1.2x-0.8x-4.8-5=0

We add all the numbers together, and all the variables

0.2x^2+0.4x-9.8=0

a = 0.2; b = 0.4; c = -9.8;
Δ = b2-4ac
Δ = 0.42-4·0.2·(-9.8)
Δ = 8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.4)-2\sqrt{2}}{2*0.2}=\frac{-0.4-2\sqrt{2}}{0.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.4)+2\sqrt{2}}{2*0.2}=\frac{-0.4+2\sqrt{2}}{0.4}
$