(3x-2)(2x-5)=-8(2x-5)

Solution for (3x-2)(2x-5)=-8(2x-5) equation:

(3x-2)(2x-5)=-8(2x-5)

We move all terms to the left:

(3x-2)(2x-5)-(-8(2x-5))=0

We multiply parentheses ..

(+6x^2-15x-4x+10)-(-8(2x-5))=0


We calculate terms in parentheses: -(-8(2x-5)), so:

-8(2x-5)

We multiply parentheses

-16x+40

Back to the equation:

-(-16x+40)


We get rid of parentheses

6x^2-15x-4x+16x+10-40=0

We add all the numbers together, and all the variables

6x^2-3x-30=0

a = 6; b = -3; c = -30;
Δ = b2-4ac
Δ = -32-4·6·(-30)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-27}{2*6}=\frac{-24}{12}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+27}{2*6}=\frac{30}{12}
=2+1/2
$