8.2x(6x-3)=7x(7x-1.2)

Solution for 8.2x(6x-3)=7x(7x-1.2) equation:

8.2x(6x-3)=7x(7x-1.2)

We move all terms to the left:

8.2x(6x-3)-(7x(7x-1.2))=0

We multiply parentheses

48x^2-24x-(7x(7x-1.2))=0


We calculate terms in parentheses: -(7x(7x-1.2)), so:

7x(7x-1.2)

We multiply parentheses

49x^2-8.4x

Back to the equation:

-(49x^2-8.4x)


We get rid of parentheses

48x^2-49x^2-24x+8.4x=0

We add all the numbers together, and all the variables

-1x^2-15.6x=0

a = -1; b = -15.6; c = 0;
Δ = b2-4ac
Δ = -15.62-4·(-1)·0
Δ = 243.36
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{-(-15.6)-\sqrt{243.36}}{2*-1}=\frac{15.6-\sqrt{243.36}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15.6)+\sqrt{243.36}}{2*-1}=\frac{15.6+\sqrt{243.36}}{-2}
$