4x^2+5x+3=2x^2+-3x

Solution for 4x^2+5x+3=2x^2+-3x equation:

4x^2+5x+3=2x^2+-3x

We move all terms to the left:

4x^2+5x+3-(2x^2+-3x)=0

We use the square of the difference formula

4x^2+5x-(2x^2-3x)+3=0

We get rid of parentheses

4x^2-2x^2+5x+3x+3=0

We add all the numbers together, and all the variables

2x^2+8x+3=0

a = 2; b = 8; c = +3;
Δ = b2-4ac
Δ = 82-4·2·3
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{10}}{2*2}=\frac{-8-2\sqrt{10}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{10}}{2*2}=\frac{-8+2\sqrt{10}}{4}
$