-5x(10-x)=35

Solution for -5x(10-x)=35 equation:

-5x(10-x)=35

We move all terms to the left:

-5x(10-x)-(35)=0

We add all the numbers together, and all the variables

-5x(-1x+10)-35=0

We multiply parentheses

5x^2-50x-35=0

a = 5; b = -50; c = -35;
Δ = b2-4ac
Δ = -502-4·5·(-35)
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-40\sqrt{2}}{2*5}=\frac{50-40\sqrt{2}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+40\sqrt{2}}{2*5}=\frac{50+40\sqrt{2}}{10}
$