2(4x^2-3)=-13x

Solution for 2(4x^2-3)=-13x equation:

2(4x^2-3)=-13x

We move all terms to the left:

2(4x^2-3)-(-13x)=0

We multiply parentheses

8x^2-(-13x)-6=0

We get rid of parentheses

8x^2+13x-6=0

a = 8; b = 13; c = -6;
Δ = b2-4ac
Δ = 132-4·8·(-6)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-19}{2*8}=\frac{-32}{16}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+19}{2*8}=\frac{6}{16}
=3/8
$