7=2x(4x-1)-1-10x

Solution for 7=2x(4x-1)-1-10x equation:

7=2x(4x-1)-1-10x

We move all terms to the left:

7-(2x(4x-1)-1-10x)=0


We calculate terms in parentheses: -(2x(4x-1)-1-10x), so:

2x(4x-1)-1-10x

determiningTheFunctionDomain
2x(4x-1)-10x-1

We add all the numbers together, and all the variables

-10x+2x(4x-1)-1

We multiply parentheses

8x^2-10x-2x-1

We add all the numbers together, and all the variables

8x^2-12x-1

Back to the equation:

-(8x^2-12x-1)


We get rid of parentheses

-8x^2+12x+1+7=0

We add all the numbers together, and all the variables

-8x^2+12x+8=0

a = -8; b = 12; c = +8;
Δ = b2-4ac
Δ = 122-4·(-8)·8
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-20}{2*-8}=\frac{-32}{-16}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+20}{2*-8}=\frac{8}{-16}
=-1/2
$