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

Solution for (2x-5)(-3x+7)=0 equation:

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

We multiply parentheses ..

(-6x^2+14x+15x-35)=0

We get rid of parentheses

-6x^2+14x+15x-35=0

We add all the numbers together, and all the variables

-6x^2+29x-35=0

a = -6; b = 29; c = -35;
Δ = b2-4ac
Δ = 292-4·(-6)·(-35)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-1}{2*-6}=\frac{-30}{-12}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+1}{2*-6}=\frac{-28}{-12}
=2+1/3
$