110-(6x+15)=6x(x+5)+x

Solution for 110-(6x+15)=6x(x+5)+x equation:

110-(6x+15)=6x(x+5)+x

We move all terms to the left:

110-(6x+15)-(6x(x+5)+x)=0

We get rid of parentheses

-6x-(6x(x+5)+x)-15+110=0


We calculate terms in parentheses: -(6x(x+5)+x), so:

6x(x+5)+x

We add all the numbers together, and all the variables

x+6x(x+5)

We multiply parentheses

6x^2+x+30x

We add all the numbers together, and all the variables

6x^2+31x

Back to the equation:

-(6x^2+31x)


We add all the numbers together, and all the variables

-6x-(6x^2+31x)+95=0

We get rid of parentheses

-6x^2-6x-31x+95=0

We add all the numbers together, and all the variables

-6x^2-37x+95=0

a = -6; b = -37; c = +95;
Δ = b2-4ac
Δ = -372-4·(-6)·95
Δ = 3649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-\sqrt{3649}}{2*-6}=\frac{37-\sqrt{3649}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{3649}}{2*-6}=\frac{37+\sqrt{3649}}{-12}
$