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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+8x^2-20x-28x+70)=0

We get rid of parentheses

8x^2-20x-28x+70=0

We add all the numbers together, and all the variables

8x^2-48x+70=0

a = 8; b = -48; c = +70;
Δ = b2-4ac
Δ = -482-4·8·70
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8}{2*8}=\frac{40}{16}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8}{2*8}=\frac{56}{16}
=3+1/2
$