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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+10x^2-15x-6x+9)=0

We get rid of parentheses

10x^2-15x-6x+9=0

We add all the numbers together, and all the variables

10x^2-21x+9=0

a = 10; b = -21; c = +9;
Δ = b2-4ac
Δ = -212-4·10·9
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-9}{2*10}=\frac{12}{20}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+9}{2*10}=\frac{30}{20}
=1+1/2
$