4x(x+5)-3(x+2)=14

Solution for 4x(x+5)-3(x+2)=14 equation:

4x(x+5)-3(x+2)=14

We move all terms to the left:

4x(x+5)-3(x+2)-(14)=0

We multiply parentheses

4x^2+20x-3x-6-14=0

We add all the numbers together, and all the variables

4x^2+17x-20=0

a = 4; b = 17; c = -20;
Δ = b2-4ac
Δ = 172-4·4·(-20)
Δ = 609
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{-(17)-\sqrt{609}}{2*4}=\frac{-17-\sqrt{609}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{609}}{2*4}=\frac{-17+\sqrt{609}}{8}
$