(-3+5x)(1+3x)=14

Solution for (-3+5x)(1+3x)=14 equation:

(-3+5x)(1+3x)=14

We move all terms to the left:

(-3+5x)(1+3x)-(14)=0

We add all the numbers together, and all the variables

(5x-3)(3x+1)-14=0

We multiply parentheses ..

(+15x^2+5x-9x-3)-14=0

We get rid of parentheses

15x^2+5x-9x-3-14=0

We add all the numbers together, and all the variables

15x^2-4x-17=0

a = 15; b = -4; c = -17;
Δ = b2-4ac
Δ = -42-4·15·(-17)
Δ = 1036
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:

$\sqrt{\Delta}=\sqrt{1036}=\sqrt{4*259}=\sqrt{4}*\sqrt{259}=2\sqrt{259}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{259}}{2*15}=\frac{4-2\sqrt{259}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{259}}{2*15}=\frac{4+2\sqrt{259}}{30}
$