(3x-5)(x+2)=2x-1

Solution for (3x-5)(x+2)=2x-1 equation:

(3x-5)(x+2)=2x-1

We move all terms to the left:

(3x-5)(x+2)-(2x-1)=0

We get rid of parentheses

(3x-5)(x+2)-2x+1=0

We multiply parentheses ..

(+3x^2+6x-5x-10)-2x+1=0

We get rid of parentheses

3x^2+6x-5x-2x-10+1=0

We add all the numbers together, and all the variables

3x^2-1x-9=0

a = 3; b = -1; c = -9;
Δ = b2-4ac
Δ = -12-4·3·(-9)
Δ = 109
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{109}}{2*3}=\frac{1-\sqrt{109}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{109}}{2*3}=\frac{1+\sqrt{109}}{6}
$