3x^2+8x+10=65

Solution for 3x^2+8x+10=65 equation:

3x^2+8x+10=65

We move all terms to the left:

3x^2+8x+10-(65)=0

We add all the numbers together, and all the variables

3x^2+8x-55=0

a = 3; b = 8; c = -55;
Δ = b2-4ac
Δ = 82-4·3·(-55)
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{181}}{2*3}=\frac{-8-2\sqrt{181}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{181}}{2*3}=\frac{-8+2\sqrt{181}}{6}
$