7x(15-x)=35

Solution for 7x(15-x)=35 equation:

7x(15-x)=35

We move all terms to the left:

7x(15-x)-(35)=0

We add all the numbers together, and all the variables

7x(-1x+15)-35=0

We multiply parentheses

-7x^2+105x-35=0

a = -7; b = 105; c = -35;
Δ = b2-4ac
Δ = 1052-4·(-7)·(-35)
Δ = 10045
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:

$\sqrt{\Delta}=\sqrt{10045}=\sqrt{49*205}=\sqrt{49}*\sqrt{205}=7\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(105)-7\sqrt{205}}{2*-7}=\frac{-105-7\sqrt{205}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+7\sqrt{205}}{2*-7}=\frac{-105+7\sqrt{205}}{-14}
$