x*(x+7)=198

Solution for x*(x+7)=198 equation:

x(x+7)=198

We move all terms to the left:

x(x+7)-(198)=0

We multiply parentheses

x^2+7x-198=0

a = 1; b = 7; c = -198;
Δ = b2-4ac
Δ = 72-4·1·(-198)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-29}{2*1}=\frac{-36}{2}
=-18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+29}{2*1}=\frac{22}{2}
=11
$