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

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

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

We multiply parentheses ..

(+3x^2-30x+7x-70)=0

We get rid of parentheses

3x^2-30x+7x-70=0

We add all the numbers together, and all the variables

3x^2-23x-70=0

a = 3; b = -23; c = -70;
Δ = b2-4ac
Δ = -232-4·3·(-70)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-37}{2*3}=\frac{-14}{6}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+37}{2*3}=\frac{60}{6}
=10
$