4(2x+7)(x-10)=0

Solution for 4(2x+7)(x-10)=0 equation:

4(2x+7)(x-10)=0

We multiply parentheses ..

4(+2x^2-20x+7x-70)=0

We multiply parentheses

8x^2-80x+28x-280=0

We add all the numbers together, and all the variables

8x^2-52x-280=0

a = 8; b = -52; c = -280;
Δ = b2-4ac
Δ = -522-4·8·(-280)
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-108}{2*8}=\frac{-56}{16}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+108}{2*8}=\frac{160}{16}
=10
$