(4x-5)*(6-7x)=0

Solution for (4x-5)*(6-7x)=0 equation:

(4x-5)(6-7x)=0

We add all the numbers together, and all the variables

(4x-5)(-7x+6)=0

We multiply parentheses ..

(-28x^2+24x+35x-30)=0

We get rid of parentheses

-28x^2+24x+35x-30=0

We add all the numbers together, and all the variables

-28x^2+59x-30=0

a = -28; b = 59; c = -30;
Δ = b2-4ac
Δ = 592-4·(-28)·(-30)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-11}{2*-28}=\frac{-70}{-56}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+11}{2*-28}=\frac{-48}{-56}
=6/7
$