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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-30x^2+3x+63=0

a = -30; b = 3; c = +63;
Δ = b2-4ac
Δ = 32-4·(-30)·63
Δ = 7569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7569}=87$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-87}{2*-30}=\frac{-90}{-60}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+87}{2*-30}=\frac{84}{-60}
=-1+2/5
$