145^2=x(81+x)

Solution for 145^2=x(81+x) equation:

145^2=x(81+x)

We move all terms to the left:

145^2-(x(81+x))=0

We add all the numbers together, and all the variables

-(x(x+81))+145^2=0

We add all the numbers together, and all the variables

-(x(x+81))+21025=0


We calculate terms in parentheses: -(x(x+81)), so:

x(x+81)

We multiply parentheses

x^2+81x

Back to the equation:

-(x^2+81x)


We get rid of parentheses

-x^2-81x+21025=0

We add all the numbers together, and all the variables

-1x^2-81x+21025=0

a = -1; b = -81; c = +21025;
Δ = b2-4ac
Δ = -812-4·(-1)·21025
Δ = 90661
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{-(-81)-\sqrt{90661}}{2*-1}=\frac{81-\sqrt{90661}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+\sqrt{90661}}{2*-1}=\frac{81+\sqrt{90661}}{-2}
$