4x+9x=24(-91/24)

Solution for 4x+9x=24(-91/24) equation:

4x+9x=24(-91/24)

We move all terms to the left:

4x+9x-(24(-91/24))=0

We add all the numbers together, and all the variables

13x-(24(-91/24))=0

We multiply all the terms by the denominator


13x*24))-(24(-91=0

Wy multiply elements

312x^2-91=0

a = 312; b = 0; c = -91;
Δ = b2-4ac
Δ = 02-4·312·(-91)
Δ = 113568
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{113568}=\sqrt{2704*42}=\sqrt{2704}*\sqrt{42}=52\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-52\sqrt{42}}{2*312}=\frac{0-52\sqrt{42}}{624}
=-\frac{52\sqrt{42}}{624}
=-\frac{\sqrt{42}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+52\sqrt{42}}{2*312}=\frac{0+52\sqrt{42}}{624}
=\frac{52\sqrt{42}}{624}
=\frac{\sqrt{42}}{12}
$