3x^2=5x+10

Solution for 3x^2=5x+10 equation:

3x^2=5x+10

We move all terms to the left:

3x^2-(5x+10)=0

We get rid of parentheses

3x^2-5x-10=0

a = 3; b = -5; c = -10;
Δ = b2-4ac
Δ = -52-4·3·(-10)
Δ = 145
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{-(-5)-\sqrt{145}}{2*3}=\frac{5-\sqrt{145}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{145}}{2*3}=\frac{5+\sqrt{145}}{6}
$