10x2=6x+3

Solution for 10x2=6x+3 equation:

10x^2=6x+3

We move all terms to the left:

10x^2-(6x+3)=0

We get rid of parentheses

10x^2-6x-3=0

a = 10; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·10·(-3)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{39}}{2*10}=\frac{6-2\sqrt{39}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{39}}{2*10}=\frac{6+2\sqrt{39}}{20}
$