x=(4x-11/2)

Solution for x=(4x-11/2) equation:

x=(4x-11/2)

We move all terms to the left:

x-((4x-11/2))=0

We add all the numbers together, and all the variables

x-((+4x-11/2))=0

We multiply all the terms by the denominator


x*2))-((+4x-11=0

We add all the numbers together, and all the variables

4x+x*2))-((-11=0

Wy multiply elements

2x^2+4x-11=0

a = 2; b = 4; c = -11;
Δ = b2-4ac
Δ = 42-4·2·(-11)
Δ = 104
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{26}}{2*2}=\frac{-4-2\sqrt{26}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{26}}{2*2}=\frac{-4+2\sqrt{26}}{4}
$