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

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

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

We multiply parentheses ..

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

We get rid of parentheses

2x^2-20x-7x+70=0

We add all the numbers together, and all the variables

2x^2-27x+70=0

a = 2; b = -27; c = +70;
Δ = b2-4ac
Δ = -272-4·2·70
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-13}{2*2}=\frac{14}{4}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+13}{2*2}=\frac{40}{4}
=10
$