x2-7x=5

Solution for x2-7x=5 equation:

x2-7x=5

We move all terms to the left:

x2-7x-(5)=0

We add all the numbers together, and all the variables

x^2-7x-5=0

a = 1; b = -7; c = -5;
Δ = b2-4ac
Δ = -72-4·1·(-5)
Δ = 69
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{-(-7)-\sqrt{69}}{2*1}=\frac{7-\sqrt{69}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{69}}{2*1}=\frac{7+\sqrt{69}}{2}
$