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

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

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

We add all the numbers together, and all the variables

(2x+3)(-1x+5)=0

We multiply parentheses ..

(-2x^2+10x-3x+15)=0

We get rid of parentheses

-2x^2+10x-3x+15=0

We add all the numbers together, and all the variables

-2x^2+7x+15=0

a = -2; b = 7; c = +15;
Δ = b2-4ac
Δ = 72-4·(-2)·15
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*-2}=\frac{6}{-4}
=-1+1/2
$