6x^2-15x+2=2^2+10x-4

Solution for 6x^2-15x+2=2^2+10x-4 equation:

6x^2-15x+2=2^2+10x-4

We move all terms to the left:

6x^2-15x+2-(2^2+10x-4)=0

We get rid of parentheses

6x^2-15x-10x+4+2-2^2=0

We add all the numbers together, and all the variables

6x^2-25x+2=0

a = 6; b = -25; c = +2;
Δ = b2-4ac
Δ = -252-4·6·2
Δ = 577
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{-(-25)-\sqrt{577}}{2*6}=\frac{25-\sqrt{577}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{577}}{2*6}=\frac{25+\sqrt{577}}{12}
$