10(5+2x)9x=80/52

Solution for 10(5+2x)9x=80/52 equation:

10(5+2x)9x=80/52

We move all terms to the left:

10(5+2x)9x-(80/52)=0

We add all the numbers together, and all the variables

10(2x+5)9x-(+80/52)=0

We multiply parentheses

180x^2+450x-(+80/52)=0

We get rid of parentheses

180x^2+450x-80/52=0

We multiply all the terms by the denominator


180x^2*52+450x*52-80=0

Wy multiply elements

9360x^2+23400x-80=0

a = 9360; b = 23400; c = -80;
Δ = b2-4ac
Δ = 234002-4·9360·(-80)
Δ = 550555200
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:

$\sqrt{\Delta}=\sqrt{550555200}=\sqrt{14400*38233}=\sqrt{14400}*\sqrt{38233}=120\sqrt{38233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23400)-120\sqrt{38233}}{2*9360}=\frac{-23400-120\sqrt{38233}}{18720}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23400)+120\sqrt{38233}}{2*9360}=\frac{-23400+120\sqrt{38233}}{18720}
$