5x^2=45-16x

Solution for 5x^2=45-16x equation:

5x^2=45-16x

We move all terms to the left:

5x^2-(45-16x)=0

We add all the numbers together, and all the variables

5x^2-(-16x+45)=0

We get rid of parentheses

5x^2+16x-45=0

a = 5; b = 16; c = -45;
Δ = b2-4ac
Δ = 162-4·5·(-45)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-34}{2*5}=\frac{-50}{10}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+34}{2*5}=\frac{18}{10}
=1+4/5
$