23x(2x+5)=6x+315

Solution for 23x(2x+5)=6x+315 equation:

23x(2x+5)=6x+315

We move all terms to the left:

23x(2x+5)-(6x+315)=0

We multiply parentheses

46x^2+115x-(6x+315)=0

We get rid of parentheses

46x^2+115x-6x-315=0

We add all the numbers together, and all the variables

46x^2+109x-315=0

a = 46; b = 109; c = -315;
Δ = b2-4ac
Δ = 1092-4·46·(-315)
Δ = 69841
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{-(109)-\sqrt{69841}}{2*46}=\frac{-109-\sqrt{69841}}{92}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(109)+\sqrt{69841}}{2*46}=\frac{-109+\sqrt{69841}}{92}
$