3x(2x+5)-23=10

Solution for 3x(2x+5)-23=10 equation:

3x(2x+5)-23=10

We move all terms to the left:

3x(2x+5)-23-(10)=0

We add all the numbers together, and all the variables

3x(2x+5)-33=0

We multiply parentheses

6x^2+15x-33=0

a = 6; b = 15; c = -33;
Δ = b2-4ac
Δ = 152-4·6·(-33)
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{113}}{2*6}=\frac{-15-3\sqrt{113}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{113}}{2*6}=\frac{-15+3\sqrt{113}}{12}
$