5x(x-1)=35

Solution for 5x(x-1)=35 equation:

5x(x-1)=35

We move all terms to the left:

5x(x-1)-(35)=0

We multiply parentheses

5x^2-5x-35=0

a = 5; b = -5; c = -35;
Δ = b2-4ac
Δ = -52-4·5·(-35)
Δ = 725
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:

$\sqrt{\Delta}=\sqrt{725}=\sqrt{25*29}=\sqrt{25}*\sqrt{29}=5\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{29}}{2*5}=\frac{5-5\sqrt{29}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{29}}{2*5}=\frac{5+5\sqrt{29}}{10}
$