(10x+7)(3x-5)=0

Solution for (10x+7)(3x-5)=0 equation:

(10x+7)(3x-5)=0

We multiply parentheses ..

(+30x^2-50x+21x-35)=0

We get rid of parentheses

30x^2-50x+21x-35=0

We add all the numbers together, and all the variables

30x^2-29x-35=0

a = 30; b = -29; c = -35;
Δ = b2-4ac
Δ = -292-4·30·(-35)
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-71}{2*30}=\frac{-42}{60}
=-7/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+71}{2*30}=\frac{100}{60}
=1+2/3
$