(x+7)(5x)=(x+7)(40)

Solution for (x+7)(5x)=(x+7)(40) equation:

(x+7)(5x)=(x+7)(40)

We move all terms to the left:

(x+7)(5x)-((x+7)(40))=0

We multiply parentheses

5x^2+35x-((x+7)40)=0


We calculate terms in parentheses: -((x+7)40), so:

(x+7)40

We multiply parentheses

40x+280

Back to the equation:

-(40x+280)


We get rid of parentheses

5x^2+35x-40x-280=0

We add all the numbers together, and all the variables

5x^2-5x-280=0

a = 5; b = -5; c = -280;
Δ = b2-4ac
Δ = -52-4·5·(-280)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-75}{2*5}=\frac{-70}{10}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+75}{2*5}=\frac{80}{10}
=8
$