(x^2-7x)=3-6x^2

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

(x^2-7x)=3-6x^2

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

7x^2-7x-3=0

a = 7; b = -7; c = -3;
Δ = b2-4ac
Δ = -72-4·7·(-3)
Δ = 133
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{-(-7)-\sqrt{133}}{2*7}=\frac{7-\sqrt{133}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{133}}{2*7}=\frac{7+\sqrt{133}}{14}
$