4x^2+8x-9=-3x^2

Solution for 4x^2+8x-9=-3x^2 equation:

4x^2+8x-9=-3x^2

We move all terms to the left:

4x^2+8x-9-(-3x^2)=0

We get rid of parentheses

4x^2+3x^2+8x-9=0

We add all the numbers together, and all the variables

7x^2+8x-9=0

a = 7; b = 8; c = -9;
Δ = b2-4ac
Δ = 82-4·7·(-9)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{79}}{2*7}=\frac{-8-2\sqrt{79}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{79}}{2*7}=\frac{-8+2\sqrt{79}}{14}
$