4x2+x-8=x2+9

Solution for 4x2+x-8=x2+9 equation:

4x^2+x-8=x2+9

We move all terms to the left:

4x^2+x-8-(x2+9)=0

We add all the numbers together, and all the variables

4x^2-(+x^2+9)+x-8=0

We get rid of parentheses

4x^2-x^2+x-9-8=0

We add all the numbers together, and all the variables

3x^2+x-17=0

a = 3; b = 1; c = -17;
Δ = b2-4ac
Δ = 12-4·3·(-17)
Δ = 205
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{205}}{2*3}=\frac{-1-\sqrt{205}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{205}}{2*3}=\frac{-1+\sqrt{205}}{6}
$