4x(3x+5)-7(3x+5)(2x-1)=0

Solution for 4x(3x+5)-7(3x+5)(2x-1)=0 equation:

4x(3x+5)-7(3x+5)(2x-1)=0

We multiply parentheses

12x^2+20x-7(3x+5)(2x-1)=0

We multiply parentheses ..

12x^2-7(+6x^2-3x+10x-5)+20x=0

We multiply parentheses

12x^2-42x^2+21x-70x+20x+35=0

We add all the numbers together, and all the variables

-30x^2-29x+35=0

a = -30; b = -29; c = +35;
Δ = b2-4ac
Δ = -292-4·(-30)·35
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-71}{2*-30}=\frac{-42}{-60}
=7/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+71}{2*-30}=\frac{100}{-60}
=-1+2/3
$