42=7(5+x)x=

Solution for 42=7(5+x)x= equation:

42=7(5+x)x=

We move all terms to the left:

42-(7(5+x)x)=0

We add all the numbers together, and all the variables

-(7(x+5)x)+42=0


We calculate terms in parentheses: -(7(x+5)x), so:

7(x+5)x

We multiply parentheses

7x^2+35x

Back to the equation:

-(7x^2+35x)


We get rid of parentheses

-7x^2-35x+42=0

a = -7; b = -35; c = +42;
Δ = b2-4ac
Δ = -352-4·(-7)·42
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-49}{2*-7}=\frac{-14}{-14}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+49}{2*-7}=\frac{84}{-14}
=-6
$