4x+3=152x^2+2=

Solution for 4x+3=152x^2+2= equation:

4x+3=152x^2+2=

We move all terms to the left:

4x+3-(152x^2+2)=0

We get rid of parentheses

-152x^2+4x-2+3=0

We add all the numbers together, and all the variables

-152x^2+4x+1=0

a = -152; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·(-152)·1
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{39}}{2*-152}=\frac{-4-4\sqrt{39}}{-304}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{39}}{2*-152}=\frac{-4+4\sqrt{39}}{-304}
$