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

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

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

We move all terms to the left:

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

We multiply parentheses

28x^2-196x-(-2(x+5))=0


We calculate terms in parentheses: -(-2(x+5)), so:

-2(x+5)

We multiply parentheses

-2x-10

Back to the equation:

-(-2x-10)


We get rid of parentheses

28x^2-196x+2x+10=0

We add all the numbers together, and all the variables

28x^2-194x+10=0

a = 28; b = -194; c = +10;
Δ = b2-4ac
Δ = -1942-4·28·10
Δ = 36516
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:

$\sqrt{\Delta}=\sqrt{36516}=\sqrt{4*9129}=\sqrt{4}*\sqrt{9129}=2\sqrt{9129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-194)-2\sqrt{9129}}{2*28}=\frac{194-2\sqrt{9129}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-194)+2\sqrt{9129}}{2*28}=\frac{194+2\sqrt{9129}}{56}
$