x*(x-5)=7

Solution for x*(x-5)=7 equation:

x(x-5)=7

We move all terms to the left:

x(x-5)-(7)=0

We multiply parentheses

x^2-5x-7=0

a = 1; b = -5; c = -7;
Δ = b2-4ac
Δ = -52-4·1·(-7)
Δ = 53
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{-(-5)-\sqrt{53}}{2*1}=\frac{5-\sqrt{53}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{53}}{2*1}=\frac{5+\sqrt{53}}{2}
$