x=(3x+35)x-5

Solution for x=(3x+35)x-5 equation:

x=(3x+35)x-5

We move all terms to the left:

x-((3x+35)x-5)=0


We calculate terms in parentheses: -((3x+35)x-5), so:

(3x+35)x-5

We multiply parentheses

3x^2+35x-5

Back to the equation:

-(3x^2+35x-5)


We get rid of parentheses

-3x^2+x-35x+5=0

We add all the numbers together, and all the variables

-3x^2-34x+5=0

a = -3; b = -34; c = +5;
Δ = b2-4ac
Δ = -342-4·(-3)·5
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-8\sqrt{19}}{2*-3}=\frac{34-8\sqrt{19}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+8\sqrt{19}}{2*-3}=\frac{34+8\sqrt{19}}{-6}
$