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

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

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

We move all terms to the left:

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

We multiply parentheses

10x^2-10x-7x-7-4=0

We add all the numbers together, and all the variables

10x^2-17x-11=0

a = 10; b = -17; c = -11;
Δ = b2-4ac
Δ = -172-4·10·(-11)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-27}{2*10}=\frac{-10}{20}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+27}{2*10}=\frac{44}{20}
=2+1/5
$