5x(x-7)=5

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

5x(x-7)=5

We move all terms to the left:

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

We multiply parentheses

5x^2-35x-5=0

a = 5; b = -35; c = -5;
Δ = b2-4ac
Δ = -352-4·5·(-5)
Δ = 1325
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:

$\sqrt{\Delta}=\sqrt{1325}=\sqrt{25*53}=\sqrt{25}*\sqrt{53}=5\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-5\sqrt{53}}{2*5}=\frac{35-5\sqrt{53}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+5\sqrt{53}}{2*5}=\frac{35+5\sqrt{53}}{10}
$