156-7x*3*5x+x*99x=1/5

Solution for 156-7x*3*5x+x*99x=1/5 equation:

156-7x*3*5x+x*99x=1/5

We move all terms to the left:

156-7x*3*5x+x*99x-(1/5)=0

We add all the numbers together, and all the variables

-7x*3*5x+x*99x+156-(+1/5)=0

Wy multiply elements

-105x^2*5+99x^2+156-(+1/5)=0

We get rid of parentheses

-105x^2*5+99x^2+156-1/5=0

We multiply all the terms by the denominator


-(105x^2*5)*5+99x^2*5-1+156*5=0

We add all the numbers together, and all the variables

99x^2*5-(105x^2*5)*5+779=0

We multiply parentheses

99x^2*5-2625x^2+779=0

Wy multiply elements

495x^2-2625x^2+779=0

We add all the numbers together, and all the variables

-2130x^2+779=0

a = -2130; b = 0; c = +779;
Δ = b2-4ac
Δ = 02-4·(-2130)·779
Δ = 6637080
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:

$\sqrt{\Delta}=\sqrt{6637080}=\sqrt{4*1659270}=\sqrt{4}*\sqrt{1659270}=2\sqrt{1659270}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1659270}}{2*-2130}=\frac{0-2\sqrt{1659270}}{-4260}
=-\frac{2\sqrt{1659270}}{-4260}
=-\frac{\sqrt{1659270}}{-2130}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1659270}}{2*-2130}=\frac{0+2\sqrt{1659270}}{-4260}
=\frac{2\sqrt{1659270}}{-4260}
=\frac{\sqrt{1659270}}{-2130}
$