5x(X-7)=45

Solution for 5x(X-7)=45 equation:

5x(x-7)=45

We move all terms to the left:

5x(x-7)-(45)=0

We multiply parentheses

5x^2-35x-45=0

a = 5; b = -35; c = -45;
Δ = b2-4ac
Δ = -352-4·5·(-45)
Δ = 2125
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:

$\sqrt{\Delta}=\sqrt{2125}=\sqrt{25*85}=\sqrt{25}*\sqrt{85}=5\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-5\sqrt{85}}{2*5}=\frac{35-5\sqrt{85}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+5\sqrt{85}}{2*5}=\frac{35+5\sqrt{85}}{10}
$