4x(x-7)=0.3(x+2)+2.11

Solution for 4x(x-7)=0.3(x+2)+2.11 equation:

4x(x-7)=0.3(x+2)+2.11

We move all terms to the left:

4x(x-7)-(0.3(x+2)+2.11)=0

We multiply parentheses

4x^2-28x-(0.3(x+2)+2.11)=0


We calculate terms in parentheses: -(0.3(x+2)+2.11), so:

0.3(x+2)+2.11

We multiply parentheses

0.3x+0.6+2.11

We add all the numbers together, and all the variables

0.3x+2.71

Back to the equation:

-(0.3x+2.71)


We get rid of parentheses

4x^2-28x-0.3x-2.71=0

We add all the numbers together, and all the variables

4x^2-28.3x-2.71=0

a = 4; b = -28.3; c = -2.71;
Δ = b2-4ac
Δ = -28.32-4·4·(-2.71)
Δ = 844.25
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{-(-28.3)-\sqrt{844.25}}{2*4}=\frac{28.3-\sqrt{844.25}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28.3)+\sqrt{844.25}}{2*4}=\frac{28.3+\sqrt{844.25}}{8}
$