(10x+7)*(1-4x)=0

Solution for (10x+7)*(1-4x)=0 equation:

(10x+7)(1-4x)=0

We add all the numbers together, and all the variables

(10x+7)(-4x+1)=0

We multiply parentheses ..

(-40x^2+10x-28x+7)=0

We get rid of parentheses

-40x^2+10x-28x+7=0

We add all the numbers together, and all the variables

-40x^2-18x+7=0

a = -40; b = -18; c = +7;
Δ = b2-4ac
Δ = -182-4·(-40)·7
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-38}{2*-40}=\frac{-20}{-80}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+38}{2*-40}=\frac{56}{-80}
=-7/10
$