11x2-10x=4-2x/2

Solution for 11x2-10x=4-2x/2 equation:

11x^2-10x=4-2x/2

We move all terms to the left:

11x^2-10x-(4-2x/2)=0

We add all the numbers together, and all the variables

11x^2-10x-(-2x/2+4)=0

We get rid of parentheses

11x^2-10x+2x/2-4=0

We multiply all the terms by the denominator


11x^2*2-10x*2+2x-4*2=0

We add all the numbers together, and all the variables

11x^2*2+2x-10x*2-8=0

Wy multiply elements

22x^2+2x-20x-8=0

We add all the numbers together, and all the variables

22x^2-18x-8=0

a = 22; b = -18; c = -8;
Δ = b2-4ac
Δ = -182-4·22·(-8)
Δ = 1028
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:

$\sqrt{\Delta}=\sqrt{1028}=\sqrt{4*257}=\sqrt{4}*\sqrt{257}=2\sqrt{257}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{257}}{2*22}=\frac{18-2\sqrt{257}}{44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{257}}{2*22}=\frac{18+2\sqrt{257}}{44}
$