4x^2-3x+16=8x+9

Solution for 4x^2-3x+16=8x+9 equation:

4x^2-3x+16=8x+9

We move all terms to the left:

4x^2-3x+16-(8x+9)=0

We get rid of parentheses

4x^2-3x-8x-9+16=0

We add all the numbers together, and all the variables

4x^2-11x+7=0

a = 4; b = -11; c = +7;
Δ = b2-4ac
Δ = -112-4·4·7
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3}{2*4}=\frac{14}{8}
=1+3/4
$