2x=3x+4x^2-10

Solution for 2x=3x+4x^2-10 equation:

2x=3x+4x^2-10

We move all terms to the left:

2x-(3x+4x^2-10)=0

We get rid of parentheses

-4x^2-3x+2x+10=0

We add all the numbers together, and all the variables

-4x^2-1x+10=0

a = -4; b = -1; c = +10;
Δ = b2-4ac
Δ = -12-4·(-4)·10
Δ = 161
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{-(-1)-\sqrt{161}}{2*-4}=\frac{1-\sqrt{161}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{161}}{2*-4}=\frac{1+\sqrt{161}}{-8}
$