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

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

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

We move all terms to the left:

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

We multiply parentheses

14x^2+10x-(3(2x+7)+4(2x-1))=0


We calculate terms in parentheses: -(3(2x+7)+4(2x-1)), so:

3(2x+7)+4(2x-1)

We multiply parentheses

6x+8x+21-4

We add all the numbers together, and all the variables

14x+17

Back to the equation:

-(14x+17)


We get rid of parentheses

14x^2+10x-14x-17=0

We add all the numbers together, and all the variables

14x^2-4x-17=0

a = 14; b = -4; c = -17;
Δ = b2-4ac
Δ = -42-4·14·(-17)
Δ = 968
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:

$\sqrt{\Delta}=\sqrt{968}=\sqrt{484*2}=\sqrt{484}*\sqrt{2}=22\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-22\sqrt{2}}{2*14}=\frac{4-22\sqrt{2}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+22\sqrt{2}}{2*14}=\frac{4+22\sqrt{2}}{28}
$