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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-3x-(5x(2x-7)+2)+6=0


We calculate terms in parentheses: -(5x(2x-7)+2), so:

5x(2x-7)+2

We multiply parentheses

10x^2-35x+2

Back to the equation:

-(10x^2-35x+2)


We get rid of parentheses

-10x^2-3x+35x-2+6=0

We add all the numbers together, and all the variables

-10x^2+32x+4=0

a = -10; b = 32; c = +4;
Δ = b2-4ac
Δ = 322-4·(-10)·4
Δ = 1184
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:

$\sqrt{\Delta}=\sqrt{1184}=\sqrt{16*74}=\sqrt{16}*\sqrt{74}=4\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{74}}{2*-10}=\frac{-32-4\sqrt{74}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{74}}{2*-10}=\frac{-32+4\sqrt{74}}{-20}
$