35-22x=x2+70

Solution for 35-22x=x2+70 equation:

35-22x=x2+70

We move all terms to the left:

35-22x-(x2+70)=0

We add all the numbers together, and all the variables

-(+x^2+70)-22x+35=0

We get rid of parentheses

-x^2-22x-70+35=0

We add all the numbers together, and all the variables

-1x^2-22x-35=0

a = -1; b = -22; c = -35;
Δ = b2-4ac
Δ = -222-4·(-1)·(-35)
Δ = 344
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:

$\sqrt{\Delta}=\sqrt{344}=\sqrt{4*86}=\sqrt{4}*\sqrt{86}=2\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{86}}{2*-1}=\frac{22-2\sqrt{86}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{86}}{2*-1}=\frac{22+2\sqrt{86}}{-2}
$