4x(2x-5)=12

Solution for 4x(2x-5)=12 equation:

4x(2x-5)=12

We move all terms to the left:

4x(2x-5)-(12)=0

We multiply parentheses

8x^2-20x-12=0

a = 8; b = -20; c = -12;
Δ = b2-4ac
Δ = -202-4·8·(-12)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-28}{2*8}=\frac{-8}{16}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+28}{2*8}=\frac{48}{16}
=3
$