3x=48-5x2

Solution for 3x=48-5x2 equation:

3x=48-5x^2

We move all terms to the left:

3x-(48-5x^2)=0

We get rid of parentheses

5x^2+3x-48=0

a = 5; b = 3; c = -48;
Δ = b2-4ac
Δ = 32-4·5·(-48)
Δ = 969
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{969}}{2*5}=\frac{-3-\sqrt{969}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{969}}{2*5}=\frac{-3+\sqrt{969}}{10}
$