45-(5x+8)=5x(x+3)+x

Solution for 45-(5x+8)=5x(x+3)+x equation:

45-(5x+8)=5x(x+3)+x

We move all terms to the left:

45-(5x+8)-(5x(x+3)+x)=0

We get rid of parentheses

-5x-(5x(x+3)+x)-8+45=0


We calculate terms in parentheses: -(5x(x+3)+x), so:

5x(x+3)+x

We add all the numbers together, and all the variables

x+5x(x+3)

We multiply parentheses

5x^2+x+15x

We add all the numbers together, and all the variables

5x^2+16x

Back to the equation:

-(5x^2+16x)


We add all the numbers together, and all the variables

-5x-(5x^2+16x)+37=0

We get rid of parentheses

-5x^2-5x-16x+37=0

We add all the numbers together, and all the variables

-5x^2-21x+37=0

a = -5; b = -21; c = +37;
Δ = b2-4ac
Δ = -212-4·(-5)·37
Δ = 1181
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{-(-21)-\sqrt{1181}}{2*-5}=\frac{21-\sqrt{1181}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{1181}}{2*-5}=\frac{21+\sqrt{1181}}{-10}
$