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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-6x^2+14x-15x+35)=0

We get rid of parentheses

-6x^2+14x-15x+35=0

We add all the numbers together, and all the variables

-6x^2-1x+35=0

a = -6; b = -1; c = +35;
Δ = b2-4ac
Δ = -12-4·(-6)·35
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{-(-1)-29}{2*-6}=\frac{-28}{-12}
=2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+29}{2*-6}=\frac{30}{-12}
=-2+1/2
$