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

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

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

We multiply parentheses ..

10(+3x^2+7x-6x-14)=0

We multiply parentheses

30x^2+70x-60x-140=0

We add all the numbers together, and all the variables

30x^2+10x-140=0

a = 30; b = 10; c = -140;
Δ = b2-4ac
Δ = 102-4·30·(-140)
Δ = 16900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16900}=130$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-130}{2*30}=\frac{-140}{60}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+130}{2*30}=\frac{120}{60}
=2
$