-82=7x(2-3x)

Solution for -82=7x(2-3x) equation:

-82=7x(2-3x)

We move all terms to the left:

-82-(7x(2-3x))=0

We add all the numbers together, and all the variables

-(7x(-3x+2))-82=0


We calculate terms in parentheses: -(7x(-3x+2)), so:

7x(-3x+2)

We multiply parentheses

-21x^2+14x

Back to the equation:

-(-21x^2+14x)


We get rid of parentheses

21x^2-14x-82=0

a = 21; b = -14; c = -82;
Δ = b2-4ac
Δ = -142-4·21·(-82)
Δ = 7084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7084}=\sqrt{4*1771}=\sqrt{4}*\sqrt{1771}=2\sqrt{1771}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{1771}}{2*21}=\frac{14-2\sqrt{1771}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{1771}}{2*21}=\frac{14+2\sqrt{1771}}{42}
$