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

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

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

We multiply parentheses ..

(+7x^2+4x-70x-40)=0

We get rid of parentheses

7x^2+4x-70x-40=0

We add all the numbers together, and all the variables

7x^2-66x-40=0

a = 7; b = -66; c = -40;
Δ = b2-4ac
Δ = -662-4·7·(-40)
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-74}{2*7}=\frac{-8}{14}
=-4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+74}{2*7}=\frac{140}{14}
=10
$