5x^2+2x+3=10+8x

Solution for 5x^2+2x+3=10+8x equation:

5x^2+2x+3=10+8x

We move all terms to the left:

5x^2+2x+3-(10+8x)=0

We add all the numbers together, and all the variables

5x^2+2x-(8x+10)+3=0

We get rid of parentheses

5x^2+2x-8x-10+3=0

We add all the numbers together, and all the variables

5x^2-6x-7=0

a = 5; b = -6; c = -7;
Δ = b2-4ac
Δ = -62-4·5·(-7)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{11}}{2*5}=\frac{6-4\sqrt{11}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{11}}{2*5}=\frac{6+4\sqrt{11}}{10}
$