9x-0,07+x^2=4x^2-1

Solution for 9x-0,07+x^2=4x^2-1 equation:

9x-0.07+x^2=4x^2-1

We move all terms to the left:

9x-0.07+x^2-(4x^2-1)=0

We get rid of parentheses

x^2-4x^2+9x+1-0.07=0

We add all the numbers together, and all the variables

-3x^2+9x+0.93=0

a = -3; b = 9; c = +0.93;
Δ = b2-4ac
Δ = 92-4·(-3)·0.93
Δ = 92.16
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{-(9)-\sqrt{92.16}}{2*-3}=\frac{-9-\sqrt{92.16}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{92.16}}{2*-3}=\frac{-9+\sqrt{92.16}}{-6}
$