4x^2-11x+16=2x+6

Solution for 4x^2-11x+16=2x+6 equation:

4x^2-11x+16=2x+6

We move all terms to the left:

4x^2-11x+16-(2x+6)=0

We get rid of parentheses

4x^2-11x-2x-6+16=0

We add all the numbers together, and all the variables

4x^2-13x+10=0

a = 4; b = -13; c = +10;
Δ = b2-4ac
Δ = -132-4·4·10
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{-(-13)-3}{2*4}=\frac{10}{8}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3}{2*4}=\frac{16}{8}
=2
$