2.5x^2=162+45x

Solution for 2.5x^2=162+45x equation:

2.5x^2=162+45x

We move all terms to the left:

2.5x^2-(162+45x)=0

We add all the numbers together, and all the variables

2.5x^2-(45x+162)=0

We get rid of parentheses

2.5x^2-45x-162=0

a = 2.5; b = -45; c = -162;
Δ = b2-4ac
Δ = -452-4·2.5·(-162)
Δ = 3645
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:

$\sqrt{\Delta}=\sqrt{3645}=\sqrt{729*5}=\sqrt{729}*\sqrt{5}=27\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-27\sqrt{5}}{2*2.5}=\frac{45-27\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+27\sqrt{5}}{2*2.5}=\frac{45+27\sqrt{5}}{5}
$