2x(10x+2)=-3(x-1)

Solution for 2x(10x+2)=-3(x-1) equation:

2x(10x+2)=-3(x-1)

We move all terms to the left:

2x(10x+2)-(-3(x-1))=0

We multiply parentheses

20x^2+4x-(-3(x-1))=0


We calculate terms in parentheses: -(-3(x-1)), so:

-3(x-1)

We multiply parentheses

-3x+3

Back to the equation:

-(-3x+3)


We get rid of parentheses

20x^2+4x+3x-3=0

We add all the numbers together, and all the variables

20x^2+7x-3=0

a = 20; b = 7; c = -3;
Δ = b2-4ac
Δ = 72-4·20·(-3)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-17}{2*20}=\frac{-24}{40}
=-3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+17}{2*20}=\frac{10}{40}
=1/4
$