(4x-5)(6x=2)

Solution for (4x-5)(6x=2) equation:

(4x-5)(6x=2)

We move all terms to the left:

(4x-5)(6x-(2))=0

We multiply parentheses ..

(+24x^2-8x-30x+10)=0

We get rid of parentheses

24x^2-8x-30x+10=0

We add all the numbers together, and all the variables

24x^2-38x+10=0

a = 24; b = -38; c = +10;
Δ = b2-4ac
Δ = -382-4·24·10
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-22}{2*24}=\frac{16}{48}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+22}{2*24}=\frac{60}{48}
=1+1/4
$