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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2+10x+7=0

a = -3; b = 10; c = +7;
Δ = b2-4ac
Δ = 102-4·(-3)·7
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{46}}{2*-3}=\frac{-10-2\sqrt{46}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{46}}{2*-3}=\frac{-10+2\sqrt{46}}{-6}
$