3x^2-10x=4x+49

Solution for 3x^2-10x=4x+49 equation:

3x^2-10x=4x+49

We move all terms to the left:

3x^2-10x-(4x+49)=0

We get rid of parentheses

3x^2-10x-4x-49=0

We add all the numbers together, and all the variables

3x^2-14x-49=0

a = 3; b = -14; c = -49;
Δ = b2-4ac
Δ = -142-4·3·(-49)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-28}{2*3}=\frac{-14}{6}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+28}{2*3}=\frac{42}{6}
=7
$