10x(x+4)-3=14x+1

Solution for 10x(x+4)-3=14x+1 equation:

10x(x+4)-3=14x+1

We move all terms to the left:

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

We multiply parentheses

10x^2+40x-(14x+1)-3=0

We get rid of parentheses

10x^2+40x-14x-1-3=0

We add all the numbers together, and all the variables

10x^2+26x-4=0

a = 10; b = 26; c = -4;
Δ = b2-4ac
Δ = 262-4·10·(-4)
Δ = 836
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:

$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{209}}{2*10}=\frac{-26-2\sqrt{209}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{209}}{2*10}=\frac{-26+2\sqrt{209}}{20}
$