3(2x-5)-3x(x-7)=2x-9

Solution for 3(2x-5)-3x(x-7)=2x-9 equation:

3(2x-5)-3x(x-7)=2x-9

We move all terms to the left:

3(2x-5)-3x(x-7)-(2x-9)=0

We multiply parentheses

-3x^2+6x+21x-(2x-9)-15=0

We get rid of parentheses

-3x^2+6x+21x-2x+9-15=0

We add all the numbers together, and all the variables

-3x^2+25x-6=0

a = -3; b = 25; c = -6;
Δ = b2-4ac
Δ = 252-4·(-3)·(-6)
Δ = 553
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{-(25)-\sqrt{553}}{2*-3}=\frac{-25-\sqrt{553}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{553}}{2*-3}=\frac{-25+\sqrt{553}}{-6}
$