2.1x+6=1.4x(4.5x-0.24)

Solution for 2.1x+6=1.4x(4.5x-0.24) equation:

2.1x+6=1.4x(4.5x-0.24)

We move all terms to the left:

2.1x+6-(1.4x(4.5x-0.24))=0


We calculate terms in parentheses: -(1.4x(4.5x-0.24)), so:

1.4x(4.5x-0.24)

We multiply parentheses

4x^2-0.24x

Back to the equation:

-(4x^2-0.24x)


We get rid of parentheses

-4x^2+2.1x+0.24x+6=0

We add all the numbers together, and all the variables

-4x^2+2.34x+6=0

a = -4; b = 2.34; c = +6;
Δ = b2-4ac
Δ = 2.342-4·(-4)·6
Δ = 101.4756
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{-(2.34)-\sqrt{101.4756}}{2*-4}=\frac{-2.34-\sqrt{101.4756}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.34)+\sqrt{101.4756}}{2*-4}=\frac{-2.34+\sqrt{101.4756}}{-8}
$