2(4x+3)(3x+5)=58x^2+58x+15

Solution for 2(4x+3)(3x+5)=58x^2+58x+15 equation:

2(4x+3)(3x+5)=58x^2+58x+15

We move all terms to the left:

2(4x+3)(3x+5)-(58x^2+58x+15)=0

We get rid of parentheses

-58x^2+2(4x+3)(3x+5)-58x-15=0

We multiply parentheses ..

-58x^2+2(+12x^2+20x+9x+15)-58x-15=0

We multiply parentheses

-58x^2+24x^2+40x+18x-58x+30-15=0

We add all the numbers together, and all the variables

-34x^2+15=0

a = -34; b = 0; c = +15;
Δ = b2-4ac
Δ = 02-4·(-34)·15
Δ = 2040
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:

$\sqrt{\Delta}=\sqrt{2040}=\sqrt{4*510}=\sqrt{4}*\sqrt{510}=2\sqrt{510}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{510}}{2*-34}=\frac{0-2\sqrt{510}}{-68}
=-\frac{2\sqrt{510}}{-68}
=-\frac{\sqrt{510}}{-34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{510}}{2*-34}=\frac{0+2\sqrt{510}}{-68}
=\frac{2\sqrt{510}}{-68}
=\frac{\sqrt{510}}{-34}
$