4x^2-x+1=15/16+1

Solution for 4x^2-x+1=15/16+1 equation:

4x^2-x+1=15/16+1

We move all terms to the left:

4x^2-x+1-(15/16+1)=0

We add all the numbers together, and all the variables

4x^2-1x+1-(15/16+1)=0

We get rid of parentheses

4x^2-1x+1-1-15/16=0

We multiply all the terms by the denominator


4x^2*16-1x*16-15+1*16-1*16=0

We add all the numbers together, and all the variables

4x^2*16-1x*16-15=0

Wy multiply elements

64x^2-16x-15=0

a = 64; b = -16; c = -15;
Δ = b2-4ac
Δ = -162-4·64·(-15)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-64}{2*64}=\frac{-48}{128}
=-3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+64}{2*64}=\frac{80}{128}
=5/8
$