17x+6=5(2x+2)7x-4

Solution for 17x+6=5(2x+2)7x-4 equation:

17x+6=5(2x+2)7x-4

We move all terms to the left:

17x+6-(5(2x+2)7x-4)=0


We calculate terms in parentheses: -(5(2x+2)7x-4), so:

5(2x+2)7x-4

We multiply parentheses

70x^2+70x-4

Back to the equation:

-(70x^2+70x-4)


We get rid of parentheses

-70x^2+17x-70x+4+6=0

We add all the numbers together, and all the variables

-70x^2-53x+10=0

a = -70; b = -53; c = +10;
Δ = b2-4ac
Δ = -532-4·(-70)·10
Δ = 5609
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{-(-53)-\sqrt{5609}}{2*-70}=\frac{53-\sqrt{5609}}{-140}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+\sqrt{5609}}{2*-70}=\frac{53+\sqrt{5609}}{-140}
$