4(x+5)(x+5)-(2x+1)=3(x-5)+180

Solution for 4(x+5)(x+5)-(2x+1)=3(x-5)+180 equation:

4(x+5)(x+5)-(2x+1)=3(x-5)+180

We move all terms to the left:

4(x+5)(x+5)-(2x+1)-(3(x-5)+180)=0

We get rid of parentheses

4(x+5)(x+5)-2x-(3(x-5)+180)-1=0

We multiply parentheses ..

4(+x^2+5x+5x+25)-2x-(3(x-5)+180)-1=0


We calculate terms in parentheses: -(3(x-5)+180), so:

3(x-5)+180

We multiply parentheses

3x-15+180

We add all the numbers together, and all the variables

3x+165

Back to the equation:

-(3x+165)


We multiply parentheses

4x^2+20x+20x-2x-(3x+165)+100-1=0

We get rid of parentheses

4x^2+20x+20x-2x-3x-165+100-1=0

We add all the numbers together, and all the variables

4x^2+35x-66=0

a = 4; b = 35; c = -66;
Δ = b2-4ac
Δ = 352-4·4·(-66)
Δ = 2281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-\sqrt{2281}}{2*4}=\frac{-35-\sqrt{2281}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{2281}}{2*4}=\frac{-35+\sqrt{2281}}{8}
$