3=2x(4x-5)

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

3=2x(4x-5)

We move all terms to the left:

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


We calculate terms in parentheses: -(2x(4x-5)), so:

2x(4x-5)

We multiply parentheses

8x^2-10x

Back to the equation:

-(8x^2-10x)


We get rid of parentheses

-8x^2+10x+3=0

a = -8; b = 10; c = +3;
Δ = b2-4ac
Δ = 102-4·(-8)·3
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*-8}=\frac{-24}{-16}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*-8}=\frac{4}{-16}
=-1/4
$