4x2+3x=1/16

Solution for 4x2+3x=1/16 equation:

4x^2+3x=1/16

We move all terms to the left:

4x^2+3x-(1/16)=0

We add all the numbers together, and all the variables

4x^2+3x-(+1/16)=0

We get rid of parentheses

4x^2+3x-1/16=0

We multiply all the terms by the denominator


4x^2*16+3x*16-1=0

Wy multiply elements

64x^2+48x-1=0

a = 64; b = 48; c = -1;
Δ = b2-4ac
Δ = 482-4·64·(-1)
Δ = 2560
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:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-16\sqrt{10}}{2*64}=\frac{-48-16\sqrt{10}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+16\sqrt{10}}{2*64}=\frac{-48+16\sqrt{10}}{128}
$