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

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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 $

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