7x(2-3x)=3(5x-1)

Solution for 7x(2-3x)=3(5x-1) equation:

7x(2-3x)=3(5x-1)

We move all terms to the left:

7x(2-3x)-(3(5x-1))=0

We add all the numbers together, and all the variables

7x(-3x+2)-(3(5x-1))=0

We multiply parentheses

-21x^2+14x-(3(5x-1))=0


We calculate terms in parentheses: -(3(5x-1)), so:

3(5x-1)

We multiply parentheses

15x-3

Back to the equation:

-(15x-3)


We get rid of parentheses

-21x^2+14x-15x+3=0

We add all the numbers together, and all the variables

-21x^2-1x+3=0

a = -21; b = -1; c = +3;
Δ = b2-4ac
Δ = -12-4·(-21)·3
Δ = 253
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{-(-1)-\sqrt{253}}{2*-21}=\frac{1-\sqrt{253}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{253}}{2*-21}=\frac{1+\sqrt{253}}{-42}
$