0.01x(x+21)-0.21=0.01(8x+21)

Solution for 0.01x(x+21)-0.21=0.01(8x+21) equation:

0.01x(x+21)-0.21=0.01(8x+21)

We move all terms to the left:

0.01x(x+21)-0.21-(0.01(8x+21))=0

We multiply parentheses

0x^2+0x-(0.01(8x+21))-0.21=0


We calculate terms in parentheses: -(0.01(8x+21)), so:

0.01(8x+21)

We multiply parentheses

0.08x+0.21

Back to the equation:

-(0.08x+0.21)


We add all the numbers together, and all the variables

x^2+x-(0.08x+0.21)-0.21=0

We get rid of parentheses

x^2+x-0.08x-0.21-0.21=0

We add all the numbers together, and all the variables

x^2+0.92x-0.42=0

a = 1; b = 0.92; c = -0.42;
Δ = b2-4ac
Δ = 0.922-4·1·(-0.42)
Δ = 2.5264
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{-(0.92)-\sqrt{2.5264}}{2*1}=\frac{-0.92-\sqrt{2.5264}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.92)+\sqrt{2.5264}}{2*1}=\frac{-0.92+\sqrt{2.5264}}{2}
$