(10x-9)(3x+2)=(5x-3)

Solution for (10x-9)(3x+2)=(5x-3) equation:

(10x-9)(3x+2)=(5x-3)

We move all terms to the left:

(10x-9)(3x+2)-((5x-3))=0

We multiply parentheses ..

(+30x^2+20x-27x-18)-((5x-3))=0


We calculate terms in parentheses: -((5x-3)), so:

(5x-3)

We get rid of parentheses

5x-3

Back to the equation:

-(5x-3)


We get rid of parentheses

30x^2+20x-27x-5x-18+3=0

We add all the numbers together, and all the variables

30x^2-12x-15=0

a = 30; b = -12; c = -15;
Δ = b2-4ac
Δ = -122-4·30·(-15)
Δ = 1944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1944}=\sqrt{324*6}=\sqrt{324}*\sqrt{6}=18\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-18\sqrt{6}}{2*30}=\frac{12-18\sqrt{6}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+18\sqrt{6}}{2*30}=\frac{12+18\sqrt{6}}{60}
$