5x^2+7x=3x^2+2

Solution for 5x^2+7x=3x^2+2 equation:

5x^2+7x=3x^2+2

We move all terms to the left:

5x^2+7x-(3x^2+2)=0

We get rid of parentheses

5x^2-3x^2+7x-2=0

We add all the numbers together, and all the variables

2x^2+7x-2=0

a = 2; b = 7; c = -2;
Δ = b2-4ac
Δ = 72-4·2·(-2)
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{65}}{2*2}=\frac{-7-\sqrt{65}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{65}}{2*2}=\frac{-7+\sqrt{65}}{4}
$