-243=-9x(10+x)

Solution for -243=-9x(10+x) equation:

-243=-9x(10+x)

We move all terms to the left:

-243-(-9x(10+x))=0

We add all the numbers together, and all the variables

-(-9x(x+10))-243=0


We calculate terms in parentheses: -(-9x(x+10)), so:

-9x(x+10)

We multiply parentheses

-9x^2-90x

Back to the equation:

-(-9x^2-90x)


We get rid of parentheses

9x^2+90x-243=0

a = 9; b = 90; c = -243;
Δ = b2-4ac
Δ = 902-4·9·(-243)
Δ = 16848
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:

$\sqrt{\Delta}=\sqrt{16848}=\sqrt{1296*13}=\sqrt{1296}*\sqrt{13}=36\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-36\sqrt{13}}{2*9}=\frac{-90-36\sqrt{13}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+36\sqrt{13}}{2*9}=\frac{-90+36\sqrt{13}}{18}
$