2x^2+x=6x+7

Solution for 2x^2+x=6x+7 equation:

2x^2+x=6x+7

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-5x-7=0

a = 2; b = -5; c = -7;
Δ = b2-4ac
Δ = -52-4·2·(-7)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-9}{2*2}=\frac{-4}{4}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+9}{2*2}=\frac{14}{4}
=3+1/2
$