4x^2+3x^2=189

Solution for 4x^2+3x^2=189 equation:

4x^2+3x^2=189

We move all terms to the left:

4x^2+3x^2-(189)=0

We add all the numbers together, and all the variables

7x^2-189=0

a = 7; b = 0; c = -189;
Δ = b2-4ac
Δ = 02-4·7·(-189)
Δ = 5292
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:

$\sqrt{\Delta}=\sqrt{5292}=\sqrt{1764*3}=\sqrt{1764}*\sqrt{3}=42\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-42\sqrt{3}}{2*7}=\frac{0-42\sqrt{3}}{14}
=-\frac{42\sqrt{3}}{14}
=-3\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+42\sqrt{3}}{2*7}=\frac{0+42\sqrt{3}}{14}
=\frac{42\sqrt{3}}{14}
=3\sqrt{3}
$