(9-x)(7x)=35

Solution for (9-x)(7x)=35 equation:

(9-x)(7x)=35

We move all terms to the left:

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

We add all the numbers together, and all the variables

(-1x+9)7x-35=0

We multiply parentheses

-7x^2+63x-35=0

a = -7; b = 63; c = -35;
Δ = b2-4ac
Δ = 632-4·(-7)·(-35)
Δ = 2989
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:

$\sqrt{\Delta}=\sqrt{2989}=\sqrt{49*61}=\sqrt{49}*\sqrt{61}=7\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-7\sqrt{61}}{2*-7}=\frac{-63-7\sqrt{61}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+7\sqrt{61}}{2*-7}=\frac{-63+7\sqrt{61}}{-14}
$