4x^2-2x+4=7x+9

Solution for 4x^2-2x+4=7x+9 equation:

4x^2-2x+4=7x+9

We move all terms to the left:

4x^2-2x+4-(7x+9)=0

We get rid of parentheses

4x^2-2x-7x-9+4=0

We add all the numbers together, and all the variables

4x^2-9x-5=0

a = 4; b = -9; c = -5;
Δ = b2-4ac
Δ = -92-4·4·(-5)
Δ = 161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{161}}{2*4}=\frac{9-\sqrt{161}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{161}}{2*4}=\frac{9+\sqrt{161}}{8}
$