x^2=25-13x/4

Solution for x^2=25-13x/4 equation:

x^2=25-13x/4

We move all terms to the left:

x^2-(25-13x/4)=0

We add all the numbers together, and all the variables

x^2-(-13x/4+25)=0

We get rid of parentheses

x^2+13x/4-25=0

We multiply all the terms by the denominator


x^2*4+13x-25*4=0

We add all the numbers together, and all the variables

x^2*4+13x-100=0

Wy multiply elements

4x^2+13x-100=0

a = 4; b = 13; c = -100;
Δ = b2-4ac
Δ = 132-4·4·(-100)
Δ = 1769
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{-(13)-\sqrt{1769}}{2*4}=\frac{-13-\sqrt{1769}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{1769}}{2*4}=\frac{-13+\sqrt{1769}}{8}
$