3x2=31x-10

Solution for 3x2=31x-10 equation:

3x^2=31x-10

We move all terms to the left:

3x^2-(31x-10)=0

We get rid of parentheses

3x^2-31x+10=0

a = 3; b = -31; c = +10;
Δ = b2-4ac
Δ = -312-4·3·10
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-29}{2*3}=\frac{2}{6}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+29}{2*3}=\frac{60}{6}
=10
$