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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

(3x+5)(-1x+7)-()=0

We add all the numbers together, and all the variables

(3x+5)(-1x+7)=0

We multiply parentheses ..

(-3x^2+21x-5x+35)=0

We get rid of parentheses

-3x^2+21x-5x+35=0

We add all the numbers together, and all the variables

-3x^2+16x+35=0

a = -3; b = 16; c = +35;
Δ = b2-4ac
Δ = 162-4·(-3)·35
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-26}{2*-3}=\frac{-42}{-6}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+26}{2*-3}=\frac{10}{-6}
=-1+2/3
$