5x(x-1)=-2(x-4)-6

Solution for 5x(x-1)=-2(x-4)-6 equation:

5x(x-1)=-2(x-4)-6

We move all terms to the left:

5x(x-1)-(-2(x-4)-6)=0

We multiply parentheses

5x^2-5x-(-2(x-4)-6)=0


We calculate terms in parentheses: -(-2(x-4)-6), so:

-2(x-4)-6

We multiply parentheses

-2x+8-6

We add all the numbers together, and all the variables

-2x+2

Back to the equation:

-(-2x+2)


We get rid of parentheses

5x^2-5x+2x-2=0

We add all the numbers together, and all the variables

5x^2-3x-2=0

a = 5; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·5·(-2)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7}{2*5}=\frac{-4}{10}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*5}=\frac{10}{10}
=1
$