5-(8x-7)+18x=31x(90+28x)-45

Solution for 5-(8x-7)+18x=31x(90+28x)-45 equation:

5-(8x-7)+18x=31x(90+28x)-45

We move all terms to the left:

5-(8x-7)+18x-(31x(90+28x)-45)=0

We add all the numbers together, and all the variables

-(8x-7)+18x-(31x(28x+90)-45)+5=0

We add all the numbers together, and all the variables

18x-(8x-7)-(31x(28x+90)-45)+5=0

We get rid of parentheses

18x-8x-(31x(28x+90)-45)+7+5=0


We calculate terms in parentheses: -(31x(28x+90)-45), so:

31x(28x+90)-45

We multiply parentheses

868x^2+2790x-45

Back to the equation:

-(868x^2+2790x-45)


We add all the numbers together, and all the variables

10x-(868x^2+2790x-45)+12=0

We get rid of parentheses

-868x^2+10x-2790x+45+12=0

We add all the numbers together, and all the variables

-868x^2-2780x+57=0

a = -868; b = -2780; c = +57;
Δ = b2-4ac
Δ = -27802-4·(-868)·57
Δ = 7926304
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:

$\sqrt{\Delta}=\sqrt{7926304}=\sqrt{16*495394}=\sqrt{16}*\sqrt{495394}=4\sqrt{495394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2780)-4\sqrt{495394}}{2*-868}=\frac{2780-4\sqrt{495394}}{-1736}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2780)+4\sqrt{495394}}{2*-868}=\frac{2780+4\sqrt{495394}}{-1736}
$