3x^2+10+10x=-13x+46

Solution for 3x^2+10+10x=-13x+46 equation:

3x^2+10+10x=-13x+46

We move all terms to the left:

3x^2+10+10x-(-13x+46)=0

We get rid of parentheses

3x^2+10x+13x-46+10=0

We add all the numbers together, and all the variables

3x^2+23x-36=0

a = 3; b = 23; c = -36;
Δ = b2-4ac
Δ = 232-4·3·(-36)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-31}{2*3}=\frac{-54}{6}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+31}{2*3}=\frac{8}{6}
=1+1/3
$