7=0.1x(x-8)

Solution for 7=0.1x(x-8) equation:

7=0.1x(x-8)

We move all terms to the left:

7-(0.1x(x-8))=0


We calculate terms in parentheses: -(0.1x(x-8)), so:

0.1x(x-8)

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-x+7=0

We add all the numbers together, and all the variables

-1x^2-1x+7=0

a = -1; b = -1; c = +7;
Δ = b2-4ac
Δ = -12-4·(-1)·7
Δ = 29
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)-\sqrt{29}}{2*-1}=\frac{1-\sqrt{29}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{29}}{2*-1}=\frac{1+\sqrt{29}}{-2}
$