10x2=7x+3

Solution for 10x2=7x+3 equation:

10x^2=7x+3

We move all terms to the left:

10x^2-(7x+3)=0

We get rid of parentheses

10x^2-7x-3=0

a = 10; b = -7; c = -3;
Δ = b2-4ac
Δ = -72-4·10·(-3)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*10}=\frac{-6}{20}
=-3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*10}=\frac{20}{20}
=1
$