4x^2/9+17=36

Solution for 4x^2/9+17=36 equation:

4x^2/9+17=36

We move all terms to the left:

4x^2/9+17-(36)=0

We add all the numbers together, and all the variables

4x^2/9-19=0

We multiply all the terms by the denominator


4x^2-19*9=0

We add all the numbers together, and all the variables

4x^2-171=0

a = 4; b = 0; c = -171;
Δ = b2-4ac
Δ = 02-4·4·(-171)
Δ = 2736
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:

$\sqrt{\Delta}=\sqrt{2736}=\sqrt{144*19}=\sqrt{144}*\sqrt{19}=12\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{19}}{2*4}=\frac{0-12\sqrt{19}}{8}
=-\frac{12\sqrt{19}}{8}
=-\frac{3\sqrt{19}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{19}}{2*4}=\frac{0+12\sqrt{19}}{8}
=\frac{12\sqrt{19}}{8}
=\frac{3\sqrt{19}}{2}
$