35=7x+5x+x^2

Solution for 35=7x+5x+x^2 equation:

35=7x+5x+x^2

We move all terms to the left:

35-(7x+5x+x^2)=0

We get rid of parentheses

-x^2-7x-5x+35=0

We add all the numbers together, and all the variables

-1x^2-12x+35=0

a = -1; b = -12; c = +35;
Δ = b2-4ac
Δ = -122-4·(-1)·35
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{71}}{2*-1}=\frac{12-2\sqrt{71}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{71}}{2*-1}=\frac{12+2\sqrt{71}}{-2}
$