-5x(x-7)=55

Solution for -5x(x-7)=55 equation:

-5x(x-7)=55

We move all terms to the left:

-5x(x-7)-(55)=0

We multiply parentheses

-5x^2+35x-55=0

a = -5; b = 35; c = -55;
Δ = b2-4ac
Δ = 352-4·(-5)·(-55)
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-5\sqrt{5}}{2*-5}=\frac{-35-5\sqrt{5}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+5\sqrt{5}}{2*-5}=\frac{-35+5\sqrt{5}}{-10}
$