x2-x+3=4x2-5

Solution for x2-x+3=4x2-5 equation:

x2-x+3=4x^2-5

We move all terms to the left:

x2-x+3-(4x^2-5)=0

We add all the numbers together, and all the variables

x^2-1x-(4x^2-5)+3=0

We get rid of parentheses

x^2-4x^2-1x+5+3=0

We add all the numbers together, and all the variables

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

a = -3; b = -1; c = +8;
Δ = b2-4ac
Δ = -12-4·(-3)·8
Δ = 97
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{-(-1)-\sqrt{97}}{2*-3}=\frac{1-\sqrt{97}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{97}}{2*-3}=\frac{1+\sqrt{97}}{-6}
$