(x-7)(3x-10)=0

Solution for (x-7)(3x-10)=0 equation:

(x-7)(3x-10)=0

We multiply parentheses ..

(+3x^2-10x-21x+70)=0

We get rid of parentheses

3x^2-10x-21x+70=0

We add all the numbers together, and all the variables

3x^2-31x+70=0

a = 3; b = -31; c = +70;
Δ = b2-4ac
Δ = -312-4·3·70
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-11}{2*3}=\frac{20}{6}
=3+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+11}{2*3}=\frac{42}{6}
=7
$