-5x+8=10x^2+6

Solution for -5x+8=10x^2+6 equation:

-5x+8=10x^2+6

We move all terms to the left:

-5x+8-(10x^2+6)=0

We get rid of parentheses

-10x^2-5x-6+8=0

We add all the numbers together, and all the variables

-10x^2-5x+2=0

a = -10; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·(-10)·2
Δ = 105
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{-(-5)-\sqrt{105}}{2*-10}=\frac{5-\sqrt{105}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{105}}{2*-10}=\frac{5+\sqrt{105}}{-20}
$