0=(34-4x+180)1x

Solution for 0=(34-4x+180)1x equation:

0=(34-4x+180)1x

We move all terms to the left:

0-((34-4x+180)1x)=0

We add all the numbers together, and all the variables

-((-4x+214)1x)+0=0

We add all the numbers together, and all the variables

-((-4x+214)1x)=0


We calculate terms in parentheses: -((-4x+214)1x), so:

(-4x+214)1x

We multiply parentheses

-4x^2+214x

Back to the equation:

-(-4x^2+214x)


We get rid of parentheses

4x^2-214x=0

a = 4; b = -214; c = 0;
Δ = b2-4ac
Δ = -2142-4·4·0
Δ = 45796
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{45796}=214$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-214)-214}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-214)+214}{2*4}=\frac{428}{8}
=53+1/2
$