X+2x(2x-10)+(2x-10/4)=180

Solution for X+2x(2x-10)+(2x-10/4)=180 equation:

X+2X(2X-10)+(2X-10/4)=180

We move all terms to the left:

X+2X(2X-10)+(2X-10/4)-(180)=0

We add all the numbers together, and all the variables

X+2X(2X-10)+(+2X-10/4)-180=0

We multiply parentheses

4X^2+X-20X+(+2X-10/4)-180=0

We get rid of parentheses

4X^2+X-20X+2X-180-10/4=0

We multiply all the terms by the denominator


4X^2*4+X*4-20X*4+2X*4-10-180*4=0

We add all the numbers together, and all the variables

4X^2*4+X*4-20X*4+2X*4-730=0

Wy multiply elements

16X^2+4X-80X+8X-730=0

We add all the numbers together, and all the variables

16X^2-68X-730=0

a = 16; b = -68; c = -730;
Δ = b2-4ac
Δ = -682-4·16·(-730)
Δ = 51344
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:

$\sqrt{\Delta}=\sqrt{51344}=\sqrt{16*3209}=\sqrt{16}*\sqrt{3209}=4\sqrt{3209}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-4\sqrt{3209}}{2*16}=\frac{68-4\sqrt{3209}}{32}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+4\sqrt{3209}}{2*16}=\frac{68+4\sqrt{3209}}{32}
$