x.2(3x-1)+2(4x+5)=7

Solution for x.2(3x-1)+2(4x+5)=7 equation:

x.2(3x-1)+2(4x+5)=7

We move all terms to the left:

x.2(3x-1)+2(4x+5)-(7)=0

We multiply parentheses

3x^2-1x+8x+10-7=0

We add all the numbers together, and all the variables

3x^2+7x+3=0

a = 3; b = 7; c = +3;
Δ = b2-4ac
Δ = 72-4·3·3
Δ = 13
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{13}}{2*3}=\frac{-7-\sqrt{13}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{13}}{2*3}=\frac{-7+\sqrt{13}}{6}
$