7(x-10)(3x+2)=0

Solution for 7(x-10)(3x+2)=0 equation:

7(x-10)(3x+2)=0

We multiply parentheses ..

7(+3x^2+2x-30x-20)=0

We multiply parentheses

21x^2+14x-210x-140=0

We add all the numbers together, and all the variables

21x^2-196x-140=0

a = 21; b = -196; c = -140;
Δ = b2-4ac
Δ = -1962-4·21·(-140)
Δ = 50176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{50176}=224$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-196)-224}{2*21}=\frac{-28}{42}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-196)+224}{2*21}=\frac{420}{42}
=10
$