4(4x+1)=2(6x+10)x-1

Solution for 4(4x+1)=2(6x+10)x-1 equation:

4(4x+1)=2(6x+10)x-1

We move all terms to the left:

4(4x+1)-(2(6x+10)x-1)=0

We multiply parentheses

16x-(2(6x+10)x-1)+4=0


We calculate terms in parentheses: -(2(6x+10)x-1), so:

2(6x+10)x-1

We multiply parentheses

12x^2+20x-1

Back to the equation:

-(12x^2+20x-1)


We get rid of parentheses

-12x^2+16x-20x+1+4=0

We add all the numbers together, and all the variables

-12x^2-4x+5=0

a = -12; b = -4; c = +5;
Δ = b2-4ac
Δ = -42-4·(-12)·5
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-16}{2*-12}=\frac{-12}{-24}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16}{2*-12}=\frac{20}{-24}
=-5/6
$