3x/10=4-x2

Solution for 3x/10=4-x2 equation:

3x/10=4-x2

We move all terms to the left:

3x/10-(4-x2)=0

We add all the numbers together, and all the variables

-(-1x^2+4)+3x/10=0

We get rid of parentheses

1x^2+3x/10-4=0

We multiply all the terms by the denominator


1x^2*10+3x-4*10=0

We add all the numbers together, and all the variables

1x^2*10+3x-40=0

Wy multiply elements

10x^2+3x-40=0

a = 10; b = 3; c = -40;
Δ = b2-4ac
Δ = 32-4·10·(-40)
Δ = 1609
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{-(3)-\sqrt{1609}}{2*10}=\frac{-3-\sqrt{1609}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{1609}}{2*10}=\frac{-3+\sqrt{1609}}{20}
$