6x2+3x=10

Solution for 6x2+3x=10 equation:

6x^2+3x=10

We move all terms to the left:

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

a = 6; b = 3; c = -10;
Δ = b2-4ac
Δ = 32-4·6·(-10)
Δ = 249
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{-(3)-\sqrt{249}}{2*6}=\frac{-3-\sqrt{249}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{249}}{2*6}=\frac{-3+\sqrt{249}}{12}
$