(2x-7)(5x-3)=0

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

(2x-7)(5x-3)=0

We multiply parentheses ..

(+10x^2-6x-35x+21)=0

We get rid of parentheses

10x^2-6x-35x+21=0

We add all the numbers together, and all the variables

10x^2-41x+21=0

a = 10; b = -41; c = +21;
Δ = b2-4ac
Δ = -412-4·10·21
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-29}{2*10}=\frac{12}{20}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+29}{2*10}=\frac{70}{20}
=3+1/2
$