6x(2-4x)+74=3x+4(2+5x)

Solution for 6x(2-4x)+74=3x+4(2+5x) equation:

6x(2-4x)+74=3x+4(2+5x)

We move all terms to the left:

6x(2-4x)+74-(3x+4(2+5x))=0

We add all the numbers together, and all the variables

6x(-4x+2)-(3x+4(5x+2))+74=0

We multiply parentheses

-24x^2+12x-(3x+4(5x+2))+74=0


We calculate terms in parentheses: -(3x+4(5x+2)), so:

3x+4(5x+2)

We multiply parentheses

3x+20x+8

We add all the numbers together, and all the variables

23x+8

Back to the equation:

-(23x+8)


We get rid of parentheses

-24x^2+12x-23x-8+74=0

We add all the numbers together, and all the variables

-24x^2-11x+66=0

a = -24; b = -11; c = +66;
Δ = b2-4ac
Δ = -112-4·(-24)·66
Δ = 6457
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{-(-11)-\sqrt{6457}}{2*-24}=\frac{11-\sqrt{6457}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{6457}}{2*-24}=\frac{11+\sqrt{6457}}{-48}
$