4x*2x-1=3x+11

Solution for 4x*2x-1=3x+11 equation:

4x*2x-1=3x+11

We move all terms to the left:

4x*2x-1-(3x+11)=0

Wy multiply elements

8x^2-(3x+11)-1=0

We get rid of parentheses

8x^2-3x-11-1=0

We add all the numbers together, and all the variables

8x^2-3x-12=0

a = 8; b = -3; c = -12;
Δ = b2-4ac
Δ = -32-4·8·(-12)
Δ = 393
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{-(-3)-\sqrt{393}}{2*8}=\frac{3-\sqrt{393}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{393}}{2*8}=\frac{3+\sqrt{393}}{16}
$