6x(7x+8)=3x+20

Solution for 6x(7x+8)=3x+20 equation:

6x(7x+8)=3x+20

We move all terms to the left:

6x(7x+8)-(3x+20)=0

We multiply parentheses

42x^2+48x-(3x+20)=0

We get rid of parentheses

42x^2+48x-3x-20=0

We add all the numbers together, and all the variables

42x^2+45x-20=0

a = 42; b = 45; c = -20;
Δ = b2-4ac
Δ = 452-4·42·(-20)
Δ = 5385
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{-(45)-\sqrt{5385}}{2*42}=\frac{-45-\sqrt{5385}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{5385}}{2*42}=\frac{-45+\sqrt{5385}}{84}
$