30x+x*x-675=0

Solution for 30x+x*x-675=0 equation:

30x+x*x-675=0

Wy multiply elements

x^2+30x-675=0

a = 1; b = 30; c = -675;
Δ = b2-4ac
Δ = 302-4·1·(-675)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-60}{2*1}=\frac{-90}{2}
=-45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+60}{2*1}=\frac{30}{2}
=15
$