2.5x(5+2.7x)=9

Solution for 2.5x(5+2.7x)=9 equation:

2.5x(5+2.7x)=9

We move all terms to the left:

2.5x(5+2.7x)-(9)=0

We add all the numbers together, and all the variables

2.5x(2.7x+5)-9=0

We multiply parentheses

4x^2+10x-9=0

a = 4; b = 10; c = -9;
Δ = b2-4ac
Δ = 102-4·4·(-9)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{61}}{2*4}=\frac{-10-2\sqrt{61}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{61}}{2*4}=\frac{-10+2\sqrt{61}}{8}
$