(0.75x^2)+(x)=(26^2)

Solution for (0.75x^2)+(x)=(26^2) equation:

(0.75x^2)+(x)=(26^2)

We move all terms to the left:

(0.75x^2)+(x)-((26^2))=0

determiningTheFunctionDomain
(0.75x^2)+x-26^2=0

We add all the numbers together, and all the variables

x+(0.75x^2)-676=0

We get rid of parentheses

0.75x^2+x-676=0

a = 0.75; b = 1; c = -676;
Δ = b2-4ac
Δ = 12-4·0.75·(-676)
Δ = 2029
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{2029}}{2*0.75}=\frac{-1-\sqrt{2029}}{1.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{2029}}{2*0.75}=\frac{-1+\sqrt{2029}}{1.5}
$