3(2x+5)(5x-2)=42

Solution for 3(2x+5)(5x-2)=42 equation:

3(2x+5)(5x-2)=42

We move all terms to the left:

3(2x+5)(5x-2)-(42)=0

We multiply parentheses ..

3(+10x^2-4x+25x-10)-42=0

We multiply parentheses

30x^2-12x+75x-30-42=0

We add all the numbers together, and all the variables

30x^2+63x-72=0

a = 30; b = 63; c = -72;
Δ = b2-4ac
Δ = 632-4·30·(-72)
Δ = 12609
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:

$\sqrt{\Delta}=\sqrt{12609}=\sqrt{9*1401}=\sqrt{9}*\sqrt{1401}=3\sqrt{1401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-3\sqrt{1401}}{2*30}=\frac{-63-3\sqrt{1401}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+3\sqrt{1401}}{2*30}=\frac{-63+3\sqrt{1401}}{60}
$