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

Solution for 2x(3x+5)-4=0 equation:

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

We multiply parentheses

6x^2+10x-4=0

a = 6; b = 10; c = -4;
Δ = b2-4ac
Δ = 102-4·6·(-4)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*6}=\frac{-24}{12}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*6}=\frac{4}{12}
=1/3
$