11.2=3x^2+18x+8/5

Solution for 11.2=3x^2+18x+8/5 equation:

11.2=3x^2+18x+8/5

We move all terms to the left:

11.2-(3x^2+18x+8/5)=0

We get rid of parentheses

-3x^2-18x+11.2-8/5=0

We multiply all the terms by the denominator


-3x^2*5-18x*5-8+(11.2)*5=0

We add all the numbers together, and all the variables

-3x^2*5-18x*5+48=0

Wy multiply elements

-15x^2-90x+48=0

a = -15; b = -90; c = +48;
Δ = b2-4ac
Δ = -902-4·(-15)·48
Δ = 10980
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:

$\sqrt{\Delta}=\sqrt{10980}=\sqrt{36*305}=\sqrt{36}*\sqrt{305}=6\sqrt{305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{305}}{2*-15}=\frac{90-6\sqrt{305}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{305}}{2*-15}=\frac{90+6\sqrt{305}}{-30}
$