(5x-7)(-6x+9)=0

Solution for (5x-7)(-6x+9)=0 equation:

(5x-7)(-6x+9)=0

We multiply parentheses ..

(-30x^2+45x+42x-63)=0

We get rid of parentheses

-30x^2+45x+42x-63=0

We add all the numbers together, and all the variables

-30x^2+87x-63=0

a = -30; b = 87; c = -63;
Δ = b2-4ac
Δ = 872-4·(-30)·(-63)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(87)-3}{2*-30}=\frac{-90}{-60}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(87)+3}{2*-30}=\frac{-84}{-60}
=1+2/5
$