-2(3x+1)=4x(x-5)

Solution for -2(3x+1)=4x(x-5) equation:

-2(3x+1)=4x(x-5)

We move all terms to the left:

-2(3x+1)-(4x(x-5))=0

We multiply parentheses

-6x-(4x(x-5))-2=0


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

4x(x-5)

We multiply parentheses

4x^2-20x

Back to the equation:

-(4x^2-20x)


We get rid of parentheses

-4x^2-6x+20x-2=0

We add all the numbers together, and all the variables

-4x^2+14x-2=0

a = -4; b = 14; c = -2;
Δ = b2-4ac
Δ = 142-4·(-4)·(-2)
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{41}}{2*-4}=\frac{-14-2\sqrt{41}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{41}}{2*-4}=\frac{-14+2\sqrt{41}}{-8}
$