10x=4+6x^2

Solution for 10x=4+6x^2 equation:

10x=4+6x^2

We move all terms to the left:

10x-(4+6x^2)=0

We get rid of parentheses

-6x^2+10x-4=0

a = -6; b = 10; c = -4;
Δ = b2-4ac
Δ = 102-4·(-6)·(-4)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2}{2*-6}=\frac{-12}{-12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2}{2*-6}=\frac{-8}{-12}
=2/3
$