(15x^2+10)-(12x+8)=0

Solution for (15x^2+10)-(12x+8)=0 equation:

(15x^2+10)-(12x+8)=0

We get rid of parentheses

15x^2-12x+10-8=0

We add all the numbers together, and all the variables

15x^2-12x+2=0

a = 15; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·15·2
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{6}}{2*15}=\frac{12-2\sqrt{6}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{6}}{2*15}=\frac{12+2\sqrt{6}}{30}
$