(4x*x)-x+11=7x+8

Solution for (4x*x)-x+11=7x+8 equation:

(4x*x)-x+11=7x+8

We move all terms to the left:

(4x*x)-x+11-(7x+8)=0

We add all the numbers together, and all the variables

(+4x*x)-x-(7x+8)+11=0

We add all the numbers together, and all the variables

-1x+(+4x*x)-(7x+8)+11=0

We get rid of parentheses

-1x+4x*x-7x-8+11=0

We add all the numbers together, and all the variables

-8x+4x*x+3=0

Wy multiply elements

4x^2-8x+3=0

a = 4; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·4·3
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4}{2*4}=\frac{4}{8}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4}{2*4}=\frac{12}{8}
=1+1/2
$