2(5x-3x)=7x2-1

Solution for 2(5x-3x)=7x2-1 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

2(+2x)-(7x^2-1)=0

We multiply parentheses

4x-(7x^2-1)=0

We get rid of parentheses

-7x^2+4x+1=0

a = -7; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·(-7)·1
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{11}}{2*-7}=\frac{-4-2\sqrt{11}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{11}}{2*-7}=\frac{-4+2\sqrt{11}}{-14}
$