42=6(x+10)x=

Solution for 42=6(x+10)x= equation:

42=6(x+10)x=

We move all terms to the left:

42-(6(x+10)x)=0


We calculate terms in parentheses: -(6(x+10)x), so:

6(x+10)x

We multiply parentheses

6x^2+60x

Back to the equation:

-(6x^2+60x)


We get rid of parentheses

-6x^2-60x+42=0

a = -6; b = -60; c = +42;
Δ = b2-4ac
Δ = -602-4·(-6)·42
Δ = 4608
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-48\sqrt{2}}{2*-6}=\frac{60-48\sqrt{2}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+48\sqrt{2}}{2*-6}=\frac{60+48\sqrt{2}}{-12}
$