4x^2+3x^2=75

Solution for 4x^2+3x^2=75 equation:

4x^2+3x^2=75

We move all terms to the left:

4x^2+3x^2-(75)=0

We add all the numbers together, and all the variables

7x^2-75=0

a = 7; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·7·(-75)
Δ = 2100
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:

$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{21}}{2*7}=\frac{0-10\sqrt{21}}{14}
=-\frac{10\sqrt{21}}{14}
=-\frac{5\sqrt{21}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{21}}{2*7}=\frac{0+10\sqrt{21}}{14}
=\frac{10\sqrt{21}}{14}
=\frac{5\sqrt{21}}{7}
$