15(x)=20-13(x)^2

Solution for 15(x)=20-13(x)^2 equation:

15(x)=20-13(x)^2

We move all terms to the left:

15(x)-(20-13(x)^2)=0

determiningTheFunctionDomain
-(20-13x^2)+15x=0

We get rid of parentheses

13x^2+15x-20=0

a = 13; b = 15; c = -20;
Δ = b2-4ac
Δ = 152-4·13·(-20)
Δ = 1265
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{-(15)-\sqrt{1265}}{2*13}=\frac{-15-\sqrt{1265}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{1265}}{2*13}=\frac{-15+\sqrt{1265}}{26}
$