5x(2x+14)=3x-14

Solution for 5x(2x+14)=3x-14 equation:

5x(2x+14)=3x-14

We move all terms to the left:

5x(2x+14)-(3x-14)=0

We multiply parentheses

10x^2+70x-(3x-14)=0

We get rid of parentheses

10x^2+70x-3x+14=0

We add all the numbers together, and all the variables

10x^2+67x+14=0

a = 10; b = 67; c = +14;
Δ = b2-4ac
Δ = 672-4·10·14
Δ = 3929
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{-(67)-\sqrt{3929}}{2*10}=\frac{-67-\sqrt{3929}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(67)+\sqrt{3929}}{2*10}=\frac{-67+\sqrt{3929}}{20}
$