100x(2x-1)=8(2x+1)+14

Solution for 100x(2x-1)=8(2x+1)+14 equation:

100x(2x-1)=8(2x+1)+14

We move all terms to the left:

100x(2x-1)-(8(2x+1)+14)=0

We multiply parentheses

200x^2-100x-(8(2x+1)+14)=0


We calculate terms in parentheses: -(8(2x+1)+14), so:

8(2x+1)+14

We multiply parentheses

16x+8+14

We add all the numbers together, and all the variables

16x+22

Back to the equation:

-(16x+22)


We get rid of parentheses

200x^2-100x-16x-22=0

We add all the numbers together, and all the variables

200x^2-116x-22=0

a = 200; b = -116; c = -22;
Δ = b2-4ac
Δ = -1162-4·200·(-22)
Δ = 31056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{31056}=\sqrt{16*1941}=\sqrt{16}*\sqrt{1941}=4\sqrt{1941}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-4\sqrt{1941}}{2*200}=\frac{116-4\sqrt{1941}}{400}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+4\sqrt{1941}}{2*200}=\frac{116+4\sqrt{1941}}{400}
$