3(x^2)-6x+0=4x+7

Solution for 3(x^2)-6x+0=4x+7 equation:

3(x^2)-6x+0=4x+7

We move all terms to the left:

3(x^2)-6x+0-(4x+7)=0

We add all the numbers together, and all the variables

3x^2-6x-(4x+7)=0

We get rid of parentheses

3x^2-6x-4x-7=0

We add all the numbers together, and all the variables

3x^2-10x-7=0

a = 3; b = -10; c = -7;
Δ = b2-4ac
Δ = -102-4·3·(-7)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{46}}{2*3}=\frac{10-2\sqrt{46}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{46}}{2*3}=\frac{10+2\sqrt{46}}{6}
$