x(34x+x-158)=-6

Solution for x(34x+x-158)=-6 equation:

x(34x+x-158)=-6

We move all terms to the left:

x(34x+x-158)-(-6)=0

We add all the numbers together, and all the variables

x(35x-158)-(-6)=0

We add all the numbers together, and all the variables

x(35x-158)+6=0

We multiply parentheses

35x^2-158x+6=0

a = 35; b = -158; c = +6;
Δ = b2-4ac
Δ = -1582-4·35·6
Δ = 24124
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:

$\sqrt{\Delta}=\sqrt{24124}=\sqrt{4*6031}=\sqrt{4}*\sqrt{6031}=2\sqrt{6031}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-158)-2\sqrt{6031}}{2*35}=\frac{158-2\sqrt{6031}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-158)+2\sqrt{6031}}{2*35}=\frac{158+2\sqrt{6031}}{70}
$