(10x-4)(7-3x)=0

Solution for (10x-4)(7-3x)=0 equation:

(10x-4)(7-3x)=0

We add all the numbers together, and all the variables

(10x-4)(-3x+7)=0

We multiply parentheses ..

(-30x^2+70x+12x-28)=0

We get rid of parentheses

-30x^2+70x+12x-28=0

We add all the numbers together, and all the variables

-30x^2+82x-28=0

a = -30; b = 82; c = -28;
Δ = b2-4ac
Δ = 822-4·(-30)·(-28)
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-58}{2*-30}=\frac{-140}{-60}
=2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+58}{2*-30}=\frac{-24}{-60}
=2/5
$