(2x+1)(x+6)=3x+7

Solution for (2x+1)(x+6)=3x+7 equation:

(2x+1)(x+6)=3x+7

We move all terms to the left:

(2x+1)(x+6)-(3x+7)=0

We get rid of parentheses

(2x+1)(x+6)-3x-7=0

We multiply parentheses ..

(+2x^2+12x+x+6)-3x-7=0

We get rid of parentheses

2x^2+12x+x-3x+6-7=0

We add all the numbers together, and all the variables

2x^2+10x-1=0

a = 2; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·2·(-1)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{3}}{2*2}=\frac{-10-6\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{3}}{2*2}=\frac{-10+6\sqrt{3}}{4}
$