3x(5+2x)-5(3x+7)=1

Solution for 3x(5+2x)-5(3x+7)=1 equation:

3x(5+2x)-5(3x+7)=1

We move all terms to the left:

3x(5+2x)-5(3x+7)-(1)=0

We add all the numbers together, and all the variables

3x(2x+5)-5(3x+7)-1=0

We multiply parentheses

6x^2+15x-15x-35-1=0

We add all the numbers together, and all the variables

6x^2-36=0

a = 6; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·6·(-36)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{6}}{2*6}=\frac{0-12\sqrt{6}}{12}
=-\frac{12\sqrt{6}}{12}
=-\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{6}}{2*6}=\frac{0+12\sqrt{6}}{12}
=\frac{12\sqrt{6}}{12}
=\sqrt{6}
$