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

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

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

We move all terms to the left:

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

We multiply parentheses

-8x-(5x(x+3))+2=0


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

5x(x+3)

We multiply parentheses

5x^2+15x

Back to the equation:

-(5x^2+15x)


We get rid of parentheses

-5x^2-8x-15x+2=0

We add all the numbers together, and all the variables

-5x^2-23x+2=0

a = -5; b = -23; c = +2;
Δ = b2-4ac
Δ = -232-4·(-5)·2
Δ = 569
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{-(-23)-\sqrt{569}}{2*-5}=\frac{23-\sqrt{569}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{569}}{2*-5}=\frac{23+\sqrt{569}}{-10}
$